Damian takes his responsibilty and I just know it is a mess when he says that because Bruce wouldn't let this happen at all and others might not trust Damian with Prime too. If Jon is also there I think he would just say WELL I GO WITH YOU GUYS TOO. And just the idea if it is hilarious. In minute 5 Prime starts to talk about how they are a new super-bat duo, Jon says he is Damian's Super and Damian just want to kill both of them.
Also considering he us actually a reader and damian borned after he created I think prime can be a lot more chill about Talia and all that stuff than others or at least be someone who doesn't see them just as a bunch of terrorists.
People not trusting Damian with Prime is so... 😭 But I can see it. The people who are still weary around him due to his history, maybe more so if his various bad future are known (The Legion of Super-Heroes calling Damian a baby Hitler... ohhh when I catch you). So, why would they trust him to "take responsibility" for someone else whose history is just as bloody?
Honestly, it could even line up with the new JLU story line, too. Pairing bad guys who want to "do better" post-DC K.O. with heroes as their sort of probation officer. Except nobody would believe a 14/15 year old Robin could keep a universe breaking Superboy under control. Of course Jon needs to tag along. As backup. Just in case. Nothing at all to do with also making sure Prime keeps his grubby hands to himself and quits trying to creep in on his spot as Damian's Super.