Practically speaking, Tim should probably stay away from Jason during the anniversary of his death. It's a tricky time, and historically, the two of them haven't handled being together while Jason's upset very well. So one of his instincts is to just stay away, let him handle his feelings however he wants, and not make it worse.

But.

He remembers what it was like, being the other Tim, in another universe, who'd almost died at the Joker's hand. The memories have lost some clarity with time, and he never knew everything about what happened, but he remembers how fucked-up inside that Tim felt, and he doesn't know if that's exactly how Jason feels now, but he - he just doesn't want Jason to be alone entirely. At the same time, he doesn't know how to approach this, which is why he ends up tailing the Red Hood at some point, dressed in a dark hoodie and jeans because he doesn't think Jason needs to be seeing Robin right now if he spots him.