Tim became Batman's latest apprentice in "A Lonely Place of Dying." He was 13 at the time. Jason had recently died. I have the impression that Jason was not much older -- maybe a year or two older than Tim when he showed up. It seemed to me that they looked about the same size when Jim Aparo was drawing first one and then the other in the late 80s, and I have the impression that the typical Gothamite never actually figured out that "Robin Number Two" had died at all! Many people probably assumed, when Tim started being seen in public, that he was "the second Robin back in action after a dry spell." If Jason had been, say, four years older and six inches taller right before he died, that probably wouldn't have worked!
As far as I know, Tim never bothered to issue any press releases saying: "Guys, I'm actually the third Robin. The second one is dead and buried." (Jim Gordon probably could tell the difference, even if we assume he hadn't already become reasonably certain of the secret identities of Batman, the first Robin, and the second Robin -- but Jim Gordon spends a heck of a lot more time in conversations with Batman and his various sidekicks than the typical resident of Gotham City!)
So if Tim is now, say, 17, then I could see Jason being a full-grown 18 or 19. Although, given the way his history got rewritten on the fly by Superboy-Prime punching a wall, who knows?