Trust is an important thing within an adventuring party. Often it's just implicitly assumed that members of the party know and trust one another - this is kind of the default for many groups of players. This sort of implicit trust even occurs regularly with groups of characters who in-story have just met one another, which can seem a little odd if you stop to think about it.
The alternative approach is to explicitly make trust an open question, and to base in-character trust on the relationships that characters have with one another in their stories. You could justify a high level of mutual trust by establishing that the adventuring group has a long history of friendship between them, or alternatively you could examine the relationships of each pair of heroes to determine which ones trust whom and how much.
This can make the game richer, as players take into account their levels of trust when determining actions such as risking themselves to save party members, or believing plot-critical stories that they tell one another. But it can also make things trickier, with complications arising if a character decides that they can't trust one of the other party members about something.
Ultimately it depends on your playing style which way you choose to go. Just be aware that there are different ways to handle in-character trust in a game, and that other players should ideally be on the same page.
Commentary by memnarch (who has not seen the movie)
Oh dang! The versus game is starting to get some overlap action. I was wondering when that might come into play some more. After all, what good is a spy in a story if they don't get caught or do any back-stabbing? That's just an informed background bit otherwise.
It feels a little odd that Rey is just telling Finn to leave though. If you catch a spy, why just let them go? Especially if they're claiming that they haven't told the enemy everything yet. I suppose it'd be a really bad idea to kill them and possibly instigate a bar-fight, but the idea isn't without precedent. Plus, if you do let them stick around, you could always deal with them later however you like.
I would say that Annie is likely the best roleplayer in the group, slightly above Sally, so I think Pete's enjoying the opportunity to metaphorically bounce off her to improve his roleplaying skills. He's really gotten better since R2-D2. To be uncharitable though, the comment feels rather mean-spirited, even if it's in character for Pete; I think only Anakin deserves that kind of comment. Princess always seemed reasonable to me, Cassian only had the pacifist hang-up, and Darth Vader pretty much always dealt with their own problems.
Commentary by Keybounce (who has not seen the movie)
[Keybounce's comments will appear here when received.]
Rey: You’re just a spy!
Finn: Listen. I didn’t know they were First Order. They started asking questions! I didn’t want them to kill me! C’mon, let’s get out of here while we can.
Rey: No, Finn. You’ve made your bed, now you have to lie in it.
Finn: I didn’t say enough to make them happy. They want me to stick with you and steal the map. If we get away I can just never report in again.
Rey: I’ve heard enough. We can’t trust you now.
Rey: Go. Leave with them. Tell them everything you know, for what good it’ll do you.
Finn: I can’t go back. Kylo Ren will kill me.
Rey: That’s not my problem now, is it?
GM: Great roleplaying Annie, and Pete especially.
Rey: I’ve wanted to say something like this to one of Annie’s characters for a looong time.