How many animated media has he appeared in. Because I feel like He has been getting the least. Mostly it's been Dick or Damian now. So far he has appeared in YJ, BTAS but has not appeared in the animated movies. It's been Damian and Dick.
But in non of these (except for the DCAU movies) he has really a big role, and the DCAU Tim is basically Jason with Tim's name attached to him. That's also likely the version of Tim most people are actually familiar with, since that is the only version (appart from the new live action version maybe) that got an origin story and some focus.
Death in the Family and the live action TV show are basically the first times we have seen something is even remotly similar to Tim's original origin put on screen.
When it comes to Steph as Robin since that's not a wonder since her turn as Robin is basically just a prologue for War Games. And when it comes to Steph as Spoiler, that so storngly linked to a comics accurate version of Tim's time as Robin, that the lack of focus for him, also means that Steph will not get much.
And when it comes to Jason, UTRH gave him more focus than Tim got in all of his animated appearances out of the DCAU sofar combined.
Ok I have to admit I don't really remember much of these movies. But still don't think that this was anywhere close to the apearences the others had.
And in non of his appearances they really ever showed what makes him different from the other Robins.
Damian was the main character of several of the New52 animated movies.
Jason had big roles in UTRH and DITF.
Dick is the most used Robin in the animated TV shows, and Barbara got also a lot of screen time in those shows.
Damian would probably be rather annoyed by this whole thing and think Tim is taking something from him, IE, he would be jealous of Tim being close to his best friend.
Kon on the other hand would probably insist on a double date with him and Cassie. He'd probably tease the hell out of Tim for "Robbing the Cradle"