Put that way, there's two obvious answers.

The first answer is that the locality of physics is being violated, contrary to his previous metaphysical belief that causal relations only applied over local neighborhoods within a reality-process.

Wherever he is, it's not adjacent to the moment in space and time of his crashing plane.  Taking things at face value, and ignoring all pranks and Conspiracies in his first attack on the problem:  Both himself and some group of people from an alternate quantum-branch or future of dath ilan, have arrived to some third place not yet named and which is unfamiliar to new arrivals.

There's no story explaining that which involves amplitudes proceeding through the local causal neighborhoods of quantum physics as he knows it.  It involves action at a distance, or even if there was a continuous action through neighborhoods, they are not the neighborhoods he knows.  They are, almost equivalently, faster than light, or sideways in time.

The second answer is that anything which could violate the physics that he knows, on this scale, ought to involve some exotic contrivance, whose origin ought to be intelligence, and not the intelligence of the dath ilan he knows.  That intelligence ought to be optimizing for something.  Then having him appear naked in a cave is not visibly optimized for much of anything in particular.  The moment he appeared could be optimized for preventing his true-Death but, like, where is all of the other optimization here?  His isekai looked like, or had been made to look like, an accident or a spontaneous phenomenon.

Do new arrivals always appear in exactly the same place?  He has already seen enough to infer that (taking the Others' words at face value) new arrivals do not appear at predictable times, or not exactly predictable times; there was a duty officer who had to come down and find him within a couple of minutes of his appearance.

Again thinking just the obvious thoughts to get them out of the way, there is from his perspective an obvious angle of attack that sort of begins to address both puzzles.

Physics as Civilization knows it is simple.  Simple theories are more likely to be correct.  Simple theories are not certain to be correct.  If you tracked planets through the night sky by eyeballing their motion, the theory you would invent to explain them is classical mechanics, which in some senses if not others is simpler than General Relativity.  But classical mechanics is false and General Relativity is true.  A simple theory that excellently fits all the evidence you know is not always correct.  Something very much like it is essentially always correct.  General Relativity is like classical mechanics and that is why it gives nearly-classical motions to planets.  But the actual simple theory is not necessarily correct.

Imagine a set of rules of physics which is like the physics that dath ilan knows, except that it contains some additional terms or downright if-then-else statements whereby two otherwise distant regions of space-time-configuration end up causally related.  Sufficiently related, indeed, that a damp cave on another planet with breathable air, could end up causally descendant from the moment of a crashing plane in dath ilan.

These laws of physics are more complicated; they should end up with less measure in Greater Reality.  But if their exceptional conditions have no influence at ordinary energies in a place like dath ilan, or if their if-then-else nature is not triggered within dath ilan, these universes of weird and complicated physics may have a dath-ilan-subpart which moves in exact synchrony with dath ilan.

Othrem's plane having crashed and truekilled him, all of him within the simple universes is gone; he continues, then, in much tinier measure, within the sort of complicated universes that have exceptional conditions that can trigger and materialize him inside a cave.

It's not a very good explanation, frankly.

Which is unfortunate, because off the top of his head, it's the only explanation Othrem sees which does not involve intelligence, which if it is involved is hiding.  Either in the sense of aliens copy-kidnapping him, or in the sense of generalized authors of generalized books; if you can't see them, it's because they don't want you to know they're there.

Reasoning gets a lot more complicated once you introduce adversarial intelligences manipulating your evidence in order to hide their own existence.  If they're sufficiently smarter than you, or maybe just smart enough to succeed at a bounded problem, you will never be able to deduce those facts that they did not want you to know.  You aren't going to get it until the Conspiracy makes a mistake, or chooses to drop a hint, which nails down at least what rough sort of Conspiracy you are inside, out of an intractably vast field of possibilities.  If they are smarter than you, as realistically applies to a lot of Conspiracies that can access exotic physics, you end up thinking what they want you to think.  You may as well table those lines of thought, pending the Conspiracy having made what looks like a mistake.

It is an obvious thought that this is exactly what They want you to think; but thinking this doesn't actually help.

So return then to the supposition that things are apparently as they are.  Othrem has materialized in this cave by a fluke of exotic physics, anthropically selected to continue his experience from where it halted in almost all other cases.

...Well, it could also be an alien artifact which wasn't deliberately hidden but which is indifferent to announcing itself, i.e., if new arrivals always materialize in the same place it is maybe worth at least checking for alien machinery in the cave.

But with this little data, it is probably futile to go on staring at the set of 'all nonobvious possibilities' / 'all adversarial possibilities' / 'all the exotic clever hypotheses that don't involve taking things at face value'.  The set is too wide; one ought to try taking things at face value first, and survey how it looks from there.

Othrem has materialized inside a cave, continuing from where he otherwise would have died; it was an event of low probability, but the higher probabilities are ones with no Othrem around to experience them.  There is no visible alien machinery to support this.  One may suppose it to be either an anthropically selected fluke of physics, or alternatively the operation of alien machinery that is indifferent to revealing itself and which happens to not be immediately visible.  Other, much wider sets of Conspiratorial possibilities can be tabled until it is more useful to think about them; until some hint of alien motive has been revealed, or some flaw of alien concealment.

(If Inga were privy to this entire line of reasoning, she would cheer when Othrem finally got to this part. "Huh, isekai. That sure is weird. Unclear how it works. Might as well get on with life, meanwhile!")

(It's worth a few minutes to at least check!  Othrem did not have this line of reasoning precomputed and was not sure in advance it would arrive to the default guessable destination!)

Consider then the Others.  What has been seen of them, what may be deduced?

They appear humanoid up to the limits of visibility.  They breathe the same air he breathes.  They speak roughly Baseline, in the sort of audio frequencies his ear is accustomed to hearing.

The Others share vast amounts of information-data-complexity with himself / dath ilan.  Off the top of his head, Othrem thinks he is being fully inclusive if he categorizes possible explanations of this correlation as 'shared causal ancestry', 'convergence', and 'filtering selection'.

Their time could descend from his own.

His time does not descend from theirs, given that their attitude toward hugs has not been historically recorded... unless they're from before the Screen?  Surely Baseline must have been redone as part of the first pass of the Screening?  But of course Othrem does not actually know that, because of the second pass of the Screening.  There is some wordless sense in which the Others somehow do not feel like his ancestors, but of course the whole point of the Screen is that ancestors should not be recognizable.

Both times could descend from a common ancestor; a mutually past dath ilan that decided, after the construction of Baseline, to optimize more around how affectionate people were toward each other, perhaps at the expense of other qualities like a stronger dependency on notebooks to assist with thinking.

Those are the straightforward explanations, the ones in which all shared information is explained by shared ancestry.

You can suppose that the Others descend from a dath ilan ancestor from before the invention of Baseline, and explain away the shared information in their mostly-shared language by saying: there was convergence in which best solutions for language-invention were found.  But unless he's missing something about language invention, surely there must have been some arbitrary choices at some point in the process... well, no, maybe they actually did graph out every sibilant and pitch and their cost to vocalize, figure out what combinations would most cheaply distinguish which basic words, in order of their expected frequency of use...

Okay, no.  Othrem isn't really buying that.  Unless the constructors of Baseline were explicitly like, 'Any time we break a tie randomly it reflects a failure on our part to think of something we should be optimizing...'  Wait, no, actually that's pretty plausible.  Othrem can absolutely imagine the language-constructors reasoning like that.  Just because he can't see all the desiderata, does not mean they are not there.

Can he imagine that this is a world that diverged from dath ilan ten thousand years earlier, and they still uniquely invented Baseline?

Othrem really wants to go 'NO WAY IN SHIT' but he is not, actually, sure.  Maybe there's just enough desiderata to optimize if you are actually a linguist.

However, more plausible-feeling is that as you start to go further back in time to locate a point in divergence, leading to less shared ancestry, you must begin to postulate filtering selection: Othrem and the Others were selected by the process that brought them here, to share a language.  This is beyond the realm of flukes and near-certainly into the realm of alien machinery and unseen intelligence; there is no quirk of physics which does that.  (Frankly, there was not going to be much of a quirk of physics that materialized him naked in a cave in any case.)

And then once you permit the concept of filtering selection at all, it permits the Others to be from much further away in multiparticle-configuration-space and maybe even from some entirely other spacetime continuum.  They could have simply been selected, from across some great swathe of locally visible Reality, to happen to speak mostly-Baseline, and to breathe the air he breathes, and to speak in frequencies his ears can hear.  Or rather, both he and they were selected according to some common filter.

Othrem thinks he is going to mostly proceed on the guess of mostly shared ancestry with dath ilan, and maybe a tiny bit of convergence where that is plausible, to explain all shared information that is visible so far.  Bringing in the postulate of selection requires a whole huge chunk of assumption about the alien machinery, and throws open the possibility-space so much wider that it's harder to work with the wild possibilities inside.  He will try to try to work with the narrower assumption 'correlation proceeds from shared ancestry' until it is visibly violated.  He is a very average person of -0.2sd and does not actually do that great with trying to actually hold sixteen wild possibilities inside his head simultaneously.

Maybe the Others do natively better than that, and that is what the notebook is for.  Othrem has not really been using the notebook so far because to start visibly recording what he is thinking, he'd have to have reasoned through possible Other Conspiracies first, or how easy they'd find it to decrypt any attempted codes he used.

Well, but having gotten this far in his reasoning, it doesn't make a lot of sense to be trying to play much of an adversarial game against the Others.  They are probably descended from, or cousin to, his own dath ilan.  For them to have been selected to be a pack of supervillains and himself the only innocent among them, is getting into the realm of generalized novels.  If they are a very sophisticated Conspiracy then he already gave himself away the moment that he froze up when hugged.

It does not totally make sense, on the face of things, to try to be Very Clever and Paranoid about this.  His hypothetical opponent would be extremely amorphous and hard to fight; and there is a more coalesced and concrete possible friend standing nearby to it, at whose expense that fighting would come.

Take the Others at face value, then.  A descendant dath ilan or a cousin to it; smarter than him, in the first case, and of unknown relative intelligence otherwise.  They have selected harder on people being affectionate to one another, which is a very defensible sort of choice for a Civilization to make; they give and receive hugs more readily, and bind to their polycules more strongly at an earlier age.

On the face of things, really, they are the ones who should be worrying about adversarialism from him, once their divergence or his past-relegation becomes known.  But they shouldn't be too worried unless there are unfortunate selection effects in play, and this is known to them.  His version of dath ilan probably has more supercriminals and non-law-abiding psychopaths than their Civilization, but those are still very rare.

Can he figure out anything else about the Others?  His reasoning may be too dominated by the overshadowing surprise of the hug.

...not really and off the top of his head.  He has just seen too little of them.  Stronger emotions generally, probably.  He sees the case for that side of that old political fight within dath ilan.

He would sort of expect his dath ilan to have a more tightly organized way of welcoming new arrivals, but also that's because his dath ilan is run by specialist professional Governance.  He really doesn't know what happens if you just take... a few thousand? a few dozen? ordinary people and have them try to Just Do Things, even things that dath ilan would consider Very Important.

Okay, now he's starting to feel the disorientation of having been totally removed from his previous context, as he notices explicitly large parts of his cache getting invalidated.  What does happen if you try to build Civilization out of a few dozen random people just doing things?

And both he and the Others are within a larger world of Aliens who are less organized and less kind, and this is possibly explained by them being less smart.  Not the ones who built the isekai machinery, as an obvious guess, but perhaps a fallen version of a civilization that did?

He knows next to nothing about them, and maybe that's because he didn't ask the right questions, but it still feels like there's some kind of gap of -- it being assumed he'd guess more, or know more, about the Aliens, than he does.  It is very noticeable how little Othrem has ended up knowing about the Aliens despite trying to ask for concrete examples about them.

And from her story, it sounded like -- the Aliens haven't noticed the Others?  Or the Others pass among them without it being an explicit First Contact situation with diplomacy?  If the Others pass among the Aliens unnoticed, and if all correlation is assumed to be due to shared ancestry, then the Aliens are also cousins of dath ilan but perhaps far more distant ones.  Sharing a humanoid shape, maybe, but who knows how much or how little else.

...Othrem would absolutely not assume he understood an Alien civilization well enough to do guerilla-optimization to their street signs.  He'd be playing a much more paranoid and cautious game to avoid being noticed, if it had been decided to maintain the unawareness of the Aliens of the Others in their midst.  But maybe there was a misleading sense of similarity that misled that Other into thinking they knew a helpful and nondisruptive course of action.  Or maybe it's an extension of the Others' increased affection -- something like, increased trust, increased jumping right into things and trying to help.  Othrem thinks that even if he felt an emotion like that, it would be easy for him to notice and override when a larger goal weighed against that; but maybe that's an illusion-of-imaginary-competence, born of him not feeling that strongly in the first place.

...the Others also think it is way more helpful to have a physical notebook than Othrem finds that.  He could think into a computer.  Physical paper?  Not nearly so helpful, not for thinking.

Othrem doesn't know what to make of this, but he is trying to notice all of the anomalies at once.

He does think that it all adds up to telling the Others he thinks he's from a cousin branch of Civilization, not their own; or drawn from a wider distribution of cousinhood than other cousin-arrivals they may have known.  In the case of an adversarial game against smarter opponents, he has already given himself away; there is little to be gained down that road, and much to be lost from distrust and ill-coordination if he tries to play the paranoid against potential friends.

Could They know that this is the sort of conclusion someone like him will come to, if put in a room to think, and offered an inconvenient paper notebook rather than a more actually cognitively useful computer notepad?

Sure.

But he'll explode that pressure-triggered explosive when he steps on it.  Freezing up and taking tiny steps won't get him across the minefield any faster, if it's not just an ordinary road.

He'll nonetheless try and take some notes on the non-Conspiracy aspects of his reasoning, on his little paper notebook, in case putting them down in outline form there still manages to jog something loose inside his mind.

(Regarding the physical notebook --

Look. You just popped up naked on an alien world. What are the odds they are going to have your preferred style of laptop with your preferred operating system and your preferred notetaking software just ready to go?

Sure, they have breathable air and decipherable language and Starter Girlfriends and 99.5% of the other things you would want, but computing hardware and software is way more individual than that. It's just too much to ask.

Hence, a notebook and a pen. Or ideally, multiple pens, in multiple colors. That's a much more reasonable thing to ask for, when you pop up naked on an alien world.

Obviously.)

(If Othrem could hear that he would infer a greater degree of Personally Specialized Diversity rather than Universally Standardized Stuff Anyone Can Use Immediately among the Others compared to his own dath ilan, but he can't so he doesn't.)

(He's not even going to comment about the fact that Girlfriends are Universally Standardized Stuff Anyone Can Use Immediately? Huh, shadow-of-Inga is surprised by that, that's the sort of thing shadow-of-Othrem would usually pick up on.)

(Girlfriends do have some standardized, universally interoperable parts.)

"Othrem?" she calls softly, tapping at his door gently, in case he's lost in thought or napping.

"The new Cave Monitor will arrive soon, my shift is ending. Would you like to stay here a while longer, or would you like to come back to the main enclave with me?"

Would this usually be a significant or difficult choice to an Other?  Or is it only a nondifficult choice, that does still preserve some element of control or autonomy?  Othrem does not see an obvious reason why he would want to stay here... unless there's an Other need for quiet time that they wouldn't have satisfied by now, maybe.

"Go to main enclave," Othrem is already responding.

...should he maybe wait until he's at the main enclave to announce himself as Otherᵀ, just to preserve his optionality about new info he might see on arrival?

"Great, then come on out when you're ready."

In the distance, a car door slams. A moment later, footsteps.

Schick opens the door.

"Heyyyyyy. Big day! New arrival! So awesome. Can't wait to meet him!"

He heads on out, carrying the notebook in which he took notes.  If obviously he'd be expected to leave that notebook behind or just tear pages, well, he wasn't planning to keep this cover anyway.

"I'm Othrem," he says to the new person.  "Hi."

That sure is a smile, there.

"Inga been treating you okay, friend?"