So the reasons for my interpretation mistakes there:
1) I didn't have dialogue in any Jaime scenes except the last one, which made it confusing

2) I saw Jaime's scenes out of order

3) Jaime's ending didn't make a lot of sense to me with everything that came before it, which is just because of bad writing, so it was pretty difficult to make sense of everything I'd seen. I figured the scene with Brienne must have involved more of a betrayal considering her reaction, him getting captured, and the tone of his ending scene

You'll see a lot of the Jaime stuff, like him getting captured on the way to KL, happen next episode... well, actually, all the Jaime stuff, since he dies.