Well there's a few reasons why Oz would target Tim over other characters. Dick may be the head of the Titans but Tim has more direct connections to all of the DC, more so then most of the Bat family. Tim has worked with and even befriended and gotten the respect of most, if not all, of the main DC heroes at one time or another. On top of that he has a connection to the supernatural elements through the likes of Secret and his skills with computers (which is what OZ is using to monitor things) could become very catostrophic for him if Tim is able to screw with that through his own memories coming back. He doesn't quiet yet see Wally as a threat but I think he knows that Tim, given his "I believe Batman is out there" mentality could lead to him, if he regained his past, seeking out other missing people and eventually finding out the truth to what's going on with the Rebirth and what OZ is up to.
On top of that because Tim is well, nice and polite and over all honest, people would believe him more then anyone else, so if he said "Something's not right here," no doubt that they would agree to help him find out what that was.
Oz may want to hold him, Bart -since Bart is connected to the Flash which helped make things possible for him, and probably a magic user, because they could be the most dangerous (for magic either Zantana or Johnny).