To be honest, Jacob didn't even have to ask. Jacob and Zoey are free people. The MC has no right to forbid them from doing anything.
The MC himself invited Zoey to the party. He invites her even though he is in a relationship. What did he expect? Zoey is an attractive girl. It would be foolish to expect none of the guys to pay attention to her.
It's not so much about whether he has the right to control their relationships, and more a bro code thing. Speaking generally, dating a friend's ex can get pretty awkward - especially if they had a tumultuous relationship the way Tremolo and Zoey did. I think asking was the right call, because it's very likely given the circumstances of their breakup that he wouldn't really be comfortable with her hanging around all the time and being with one of his friends - regardless of whether he's already dating someone else or not.
That said, the good karma of asking before taking his shot is kind of immediately ruined by trying anyway, regardless of Tremolo's response. It's not that he
has to respect the guy's wishes over his own feelings, but at that point all you were really doing was trying to ease your own conscience and you didn't actually care about the answer. Which is kind of shitty.
What annoys me about this situation is something else. I don't like that I don't have the option to say: "I don't want you to date her because I want to date her myself." Given that Jacob later reveals the conversation to Zoey, this would have resulted in the MC and Zoey having sex in a tent that same night, as it should be.
I don't think they would've ended up banging even if Jacob had outright told her the MC still has feelings for her. Remember that she didn't really understand her own feelings at the time, and freaked out and ran into the woods when Tremolo told her she was his first love; this is foreshadowed in the episode's introduction, so it wouldn't really make sense if one of the possible outcomes was the two of them getting back together right then and there.
What bothers me about the choice is that, narratively, it doesn't really matter all that much. No matter what you say, the same event still occurs and goes exactly the same way in that moment.
What I'd have loved to see is, if you ask him not to, Jacob respects that and holds back... for now. He can't stop himself from feeling how he feels, of course, but he respects his friend enough to not just immediately go and do something he was specifically asked not to. Instead, if you ask him not to make a move he does so at the Christmas party; the feelings haven't gone away, and seeing her walk around in some very sexy lingerie is just too much for him to resist. Maybe at that point if Tremolo is already committed to someone else or has shown absolutely zero interest in her she takes Jacob up on the offer, or maybe she just always turns him down. But I think that would've been a much more narratively sensible order of events than the exchange going:
"Hey man, can I ask your ex out?"
"I'd prefer you didn't."
"Oh, okay, that's cool."
Ten minutes later...
"Hey baby, wanna fuck?"