Actually, we are not talking about this scene enough. I don't think what J did was romantic, and neither does the show. And honestly, the way they act before, during, and after the reveal is very telling of this!
First of all, I am absolutely going to defend Jerome a little. He thinks he's getting visions of the future, right, and it's seeping into his real life in ways he's not able to untangle. And then he gets this nugget of information. A solid piece of the puzzle, which will prove to him, once and for all, that he is not actually going crazy, what is happening to him is real. He is desperate for it. Farm might believe him, no questions asked, but this is material proof.
Which he needs so badly, he can't even wait till they're inevitably back in Jinn's condo, he needs it now!
You can see his internal struggle! Does he know he's crossing a line? Maybe. But beyond that, if he finds this notebook/diary, then he knows for sure he's seeing the future and has to live with that knowledge, aka, he has a power beyond his control and only unsure ways in which he can affect it. I'm actually surprised not many people have spoken about this.
Because when he opens the diary (it really doesn't look like he's opened beyond the first page, because Jinn opens the door almost immediately, and J was brewing on if he should at all for so long), his intention, I don't think, was to find out what Jinn had specifically written about him.
As a reminder, this is all he knows about this Diary from his visions.
He doesn't know where the rants about him are, he doesn't know what kinds of frustrations Jinn has about who, and he wants to see that it's the same diary he was talking about. And even if he does, he knows he's done a lot of complaint-worthy things throughout their youth, including but not limited to teasing him every day, stealing his crushes, and making everything a competition, and to his knowledge, their future relationship could be something that they overcame despite the genuine animosity.
And page one, he sees something unexpected.
Does this look like the face of someone who intended to uncover his oldest frenemy's deepest hidden secret?
Coz to me it looks like he's realised he fucked up big time. He sees why this was such a big deal and why future Jinn probably waited however long into their relationship to show it to Jerome. It was uncalled for. He'd crossed a boundary and broken their relationship by reading just one page, hell, one line. He'd ruined whatever delicately crafted dynamic Jinn had created to keep J from finding out he still likes him. And he's not happy about it!!!! (LOOK AT HIS FACE)
And the worst thing for him. He cannot keep lying to himself anymore. Because he's an asshole, but he loves Jinn. He doesn't know it yet, and he might not be ready to admit it. But he will not take advantage of his feelings. He now has to figure out his own feelings- not what he feels in his dreams, not what he felt when they were kids, but what he feels for Jinn in the present has to be out and in the open for their relationship to continue.
Now that he knows Jinn still likes him, their relationship is forever changed, and Jerome is not ready for it to change!
But he still has to acknowledge that it has.