So Phēl does work for some kind of Osirian intelligence agency; that explains why she hasn't introduced herself with a title or office (or agency affiliation). It presumably isn't her real name, or face, voice or species for that matter.
Intelligence services on Golarion (and probably the police, and everyone else who's legally allowed to?) operate by overwriting the minds of their targets to trust and cooperate with the investigators. This follows from being able to overwrite minds, and is really a much more civilized way of doing things than threats and physical coercion; when coercion is the nature of the game, it is better to reach the goal gently and (hopefully) reversibly.
Has Tanya's mind been overwritten to trust and cooperate with Phēl? Quite possibly! She thinks she'd notice it happening, but then her memories of it could be erased. Either way it wouldn't help anything to ask. She knew the stakes when she went to the palace for help, and they justify the risk.
"I can test magic detection against your defenses, once I'm outside the Dome. I can't tell what the spells are doing, but recognizing and tracking a signature is easy. The radar works on the same principle. Our best mages can learn to suppress mana emissions, but not perfectly and not while casting many powerful spells; I don't know if it would transfer."
"If you extract a whole community its disappearance will be noticed eventually, but that could mean hours or many days, and the first people to notice might not do anything useful with the information. If you deliberately target the most remote and out-of-touch communities you can find, it could easily be weeks, although the people there are unlikely to know much about the rest of the country; ideally you'd want to pick up some representatives of the central government... Since you're cooperating with the locals in this scenario, they would know best. Logistically, it is certainly possible for one or several villages if all you want is to collect information; when the authorities notice the disappearance they won't have a clue how it happened or a way to track you directly if you teleport far away. I don't know what their government would do, or even what it can do, once it becomes aware of the phenomenon. The risk to Osirian citizens, at present, is only that one of them could try to contact the enemy! If they give them information about Golarion or, worse, a way to contact it themselves or travel here, all bets are off." Can we get this meeting back on the track of stopping the functionally-insane Nethysians before discussing long-term spying and humanitarian efforts?
"Evacuating the population at scale would require, at minimum, somewhere to put them all - land, housing, food and work for up to a hundred million people. And you'd be picking up all the true believers and their - existing social structures, along the way. They do have a cult of personality of their current ruler; they don't call it religion but it's similar in many respects... It seems much easier to liberate their lands and keep the people where they are, but then I'm a soldier and think in those terms - and I still don't know your capabilities. For detailed information on the enemy's internal security, and everything else really, you should approach Germanian intelligence. If Osirion formally contacts Germania, I believe sharing intelligence is something friendly countries can do without having to reveal anything about their own operations. As a soldier, most of what I know myself pertains to their army." Please talk to the people whose actual job it is to be blamed for interplanetary diplomatic incidents such as 'Osirion decides to side with the Federation'.