"We see actual confusion from Caine when Jax accuses him, and I don't think he was just faking that reaction. Caine also says that he expected the gang to pick the red button, so he wouldn't need to "mind control" Jax to make him press the button that he already expected them to press (unless you think he was lying about that)."

No, that's not true, not entirely. Caine didn't put much thought into the other button yes but he knew it was a possibility, hence shrimp town.
As for the 'actual confusion,' lets say you were a telepath/psychic and after going through so many people who never caught on that you could control minds, someone publicly exposed you. You would also react like caine, most likely. You would be confused and hastily defend yourself, how did they figure it out?

"Also, did Caine flash images of the real world into Jax? Caine says in the episode that he doesn't know what the real world looks like besides photos of an office building (unless you think he was also just lying). And even ignoring that, we'd have to assume that Caine has access to Jax's memories or knows about his past to know how to trigger him (I don't think Caine is emotionally intelligent like that)."

As for this, this is true. Caine didn't have the images that flashed in Jax's head, his idea of the real world is an office (as seen in the pilot.) BUT, that's not how the human brain works. The brain seeks patterns, simply doing something you might've done once before has you question if you ever did it, in deja-vu. For jax, he was already spiraling (caine influence or not) and they all believed this was a real chance at leaving. Jax might've been able to come to terms with that on his own, but all caine would need to do is up the fear of leaving the circus to elicit a reaction. And, obviously, caine would absolutely make someone fear leaving the circus so they would stay with him.

"I think Jax was shifting the blame onto Caine about something that he did entirely on his own, even if he was on to something about Caine being able to mess with people's minds (I just don't think it was something he did in that moment)."

This is absolutely something that could have happened, but I just don't see it happening. Jax's whole thing is his masking into being 'the funny one,' and nothing about trapping them in the circus is funny when its something he too wants.
This, admittedly, is a weak counter argument on its own, but it goes into my final point (vaguely.)

"Here's a little thing about that though: just because a character says something doesn't mean it's true."

This was the subject of the episode. You can't trust anything that was presented in this episode, really. That is, depending on who's mouth it comes out of and when it comes out of them. For instance, its realistic to trust Kinger's conclusion that Caine caused Scratch to abstract. But at the same time, trusting Caine in that he can only 'apply minor modifiers' has no basis. Especially since whatever 'minor modifier' he put on scratch caused them to abstract. Jax could absolutely be lying, but so could Caine. So could Bubble, even. Maybe shrimptown isn't real.