Well, I don't really know the detail myself so I just copy-paste Tim fans' answer about Tim's role in finding Bruce.
this panel (red robin issue 12 present-day) shows that Alfred and Dick already knew. (meaning they had already found evidence of Bruce's survival while Tim was in Europe.)
the second picture is from the return of Bruce Wayne (by Grant Morrison) where Morrison directly references the bat symbol Tim found in Europe.
all Issue 12 adds is Tim finding the picture of Mordecai Wayne right after he was fired from being robin. this is how Tim knew Bruce was stranded in time.
I think Tim indeed is the one who found the evidence that Bruce is still alive first, but it's not fair to belittle Dick for it, even creating false info that Dick wanted to throw Tim into Arkham. Dick is the eldest, and as the eldest, he has responsibilities to handle everything that Bruce left behind (including 10 years old murderous son) to move forward. He has no time to investigate thing that based on vague proof.