And Oliver thinks.
And then thinks some more.
Oliver has not, at this point, mentioned in front of Emily that Leah was awake. Even without the jealousy thing--and Leah being awake and coming from Oliver's own reality would obviously make Emily even more worried--Oliver wouldn't just pop out with that fact, because Leah asked for a private conversation, and by default, you don't repeat facts from private conversations. Oliver might, but he'd need a reason. Oliver prides himself on being an unusually honest and exceptionally ethical human being that way; he'll only do unethical things for reasons, or by accident because he didn't notice, which he's pretty sure puts him in the top 5% of all human beings ethics-wise.
It's like how Oliver didn't just lie to Emily that he wouldn't sleep with Leah. Leah is pretty and looks older and also is the other person here who's already a complex realized adult. Oliver might, in fact, hit that. So Oliver will only lie about that to Emily if he decides to. He's a great human being that way!
...but before Oliver hit that, he'd first consider the question of whether he was sticking his dick in crazy.
"Stop. WAKING THEM UP!"
Now that Oliver thinks about, somebody who is otherwise leading a really comfortable life that they want to keep... is a pretty good candidate for somebody who'd go to very dangerous lengths to preserve that very comfortable life.
And if Oliver goes back and tells Leah that he has been getting what look like the start of quest chains, that his coming here coincided with JojaMart opening and the bus breaking down and the Mayor giving him the Community Center to repair? That this world may be a game, and with Oliver here, that game is starting and may not have a keepable status quo? Well, Leah could easily be the sort of person who tries to shoot the messenger about that, and just refuses to believe that it's not Oliver's fault, because Oliver is right there to be blamed, right.
Stop waking them up...