Curate, connect, and discover
OMG YEAH, at first they didn't thought a lot abt it. It was like "oh, lmao I guess he heard it from someone else" or "huh, I don't remember I ever told him that.. Welp, *ignores it*" but at some point: or they don't really care or they start finding it really odd.
Even more when he mixes something from the fanon, and they're so confused that they start putting more attention to things he shouldn't know. I think Tim and Damian would be the most confused and, idk, upset? Frustrated? ones. Because how the fuck does he know something they never told him. And I don't think Jason's even really conscious about those things that he shouldn't know
Jason: ... somewhere I must've heard it. I don't know.
Tim:
Jason: I SAID I DON'T KNOW. *leaves*