Caine does a lot of fucked up stuff but I REALLY don't think Caine altered Jax mind to press the red button.
The flashes of the real world that seem to have been the final push for Jax to act was not an office, and All Caine has to work with is office pictures.
Is why his first attempt to 'make an exit' in episode one had Pomnie go over a million different versions of an office.
Caine is very creative, he was designed to entertain, why would he recycle the same environment again and again with Pomnie's prototype exit adventure if he had access to streets, trees, houses, street signs, and car headlights? All things that despite Caine not relating to the 'macroverse' are things that Jax sees:
It could be that he tried a more indirect type of mind manipulation. A nudge that allows Jax's own mind to fill in the blanks and achieve the intended response of not wanting to leave! But that's not how Caine work.
Every single time he had tweeked people's mind it had been for the sake of adventure immersion, and when it wasn't for that, it had felt either eerily passive, or not subtle at all.
Pomnie being possessed in the haunted mansion adventure was an extremely direct and cruel way to control her mind but it fit the horror setting, it follows the rules of the high stakes adventures that theoretically anyone that picked the 'hardmode' door wanted.
Gangle's happy mask and the stupid sauce show Caine has this tremendous power outside adventure settings but they were both items that the person could chose to equip/use, not direct mind influencers, both seem to have been created to please the user as well, not put them in distress or increase the 'stakes' of their non existent non adventure related circus lives.
Caine's own distress doesn't seem to affect the player's mind, only the surroundings. Notice how everything EXCEPT the freaked out Zooble glitches here:
All the other times he freak out (like when Zooble asked for them to be able to have sex or his program crashed from jax 'being interested in his hobbies') Caine own freak out did not affect the characters minds, so influencing people's mind need to be intentional, it won't happen if he just 'wished' people reacted certain ways.
As for Caine direct and intentional modifiers, they have always been eerily passive. Jax did not feel any pain or sense of wrongness when he was turned vegan, there was no headache, no body alterations, just a sense of 'are you kidding me? why is this a possibility?' because of the idea Jax was presented with.
Which is clearly not a reaction Caine created. He just gave Jax the scenario that made Jax's mood considerably drop.
If he wasn't explicitly told 'hey buddy you're vegan now!' Jax probably wouldn't even had noticed until it directly restricted his actions. Just like Pomnie didn't realize her name was missing until Caine directly asked 'Newcomer! What's your name?' putting the issue on the spotlight.
Predictably Pomnie freaked out about it, but again, that's a natural Pomnie reaction to a fucked up situation. Caine is influencing her mind by puting her in these situations not directly comanding her to act a certain way.
So far, during this era we are witnessing at least, Caine has never directly, non consentually (you cannot convince me he scheamed very evilly for the stupid sauce to land on Ragatha's eye during the fast food episode, that was an accident) influenced someone's feelings. Hence why he is always panicked when what he gets isn't a reaction he wants to see:
And he tries to fix it by changing the surroundings and trying to prove that he is cool and good at his job!! Not explicitly changing their feelings.
Now let's go back to Jax.
why in the ever loving hell would Jax both 1 - press the red button, and 2 - freak out about mind control, if Caine didn't actually mess with his mind?
Jax intense panic in the 'exit room' parallels how he acted in the end of episode 6 after his fight with Pomnie. It is extremelly violent and human, compared to Caine's 'mind influence' powers (which I assume even at its most powerful, would still not feel like 'human panic' but closer to the trippy, inhuman, 'artificial' near abstraction trip Jax went through.)
Speculation on how Caine's mind breaking powers would feel like aside, when Jax teamed up with Pomnie he was having fun, he teased her and even opened up to her about his trypophobia and his view on the circus: He likes spending time with her. He wanted to be her friend.
A friend is something that he genuinaly craves, and therefore can genuinely hurt him, so he avoided having any. People in the circus already sees him a jerk, a bully, they don't want to be his friend, to get close to him, so is like his self destructive urges were rusty, he only realized that he started to want something when pomnie hugged him and once that realization that having a friend is possible hit, he put his walls back up full force! Shot himself in the foot to not get what he wants.
The idea of finding an exit must have been waaay more absurd to Jax than the idea of making a new friend, he barely reacted to the escape news, he didn't even want to leave his room.
He clearly doesn't believe leaving is possible and you can feel his skepticism through the entire episode 7, "this is just one of Caine's adventures" "sure let's follow mr. obvious twist villain" and so on, so on, but despite this reluntance, there are plenty of moments where Jax pauses.
When he sees Caine's 'office door', when he sees the globes with everyone's adventures, including the ones he went with his now lost friends, is like little doubts start to invade his mind '...What if this is really caine's room?' 'What if there really is a way out?' which all comes crashing down when they reach the 'hidden room' with the option to leave. Leaving is an actual option, a 'real' possibility, inside the room.
Jax wasn't lying when he said Caine messed with his head but it wasn't literally: This adventure planted in his head an idea he had throw away a long long time ago, something he really wanted and gave up on: An exit.
But if it's something he wants, why pick the 'lock us in the hell circus' button? Because when Jax wants something, genuinely wants something, he pushes it away.
I also don't think Jax can handle a 'real world with real people' after seeing others (including himself) through '2 dimensional cartoon characters' lenses. So he had this gigantic crisis only to learn that it was all fake. He 'betrayed' everyone for nothing. He really was right all along, he should have never cared.
So while we did get confirmation Caine used to modify people's mind far more drastically in the past, I don't think this was the case here, besides how such direct control for selfish reasons never happening before in the show, Caine also looks genuinely confused by Jax accusation.
He was nervous (ACTUALLY NERVOUS THAT'S VERY RARE FOR Caine) when he explained about extreme mind changes, heavily implying that doing such alterations was a MISTAKE and that he wouldn't do it again, (AI don't do things that they RECOGNIZE as mistakes) as show on his clumsy, extremelly flawed, but genuine attempts to learn how to make the players happy.