That is a very good question. 

I could create a loose timeline if it’ll be useful utility for us, but for now we can assume that Jason (as Red Hood) has been active for a minimum of five years. This allows his “Under the Red Hood” shenanigans be done and over with and at this point Jason has been travelling around the world to figure out who he is. He may have only returned to Gotham recently to look over his old neighborhood and get things sorted without being a problem for Bruce. This suggest any working relationships he has with Tim Drake to possibly be minimal, but Tim has been operating for a few years now and was likely someone he has had an interaction or two with. I’d argue Jason has more of an opinion and rivalry with Dick, though.