One could argue that after what Tarkin did to that Imperial facility, the Emperor might instruct Vader to keep a close eye on him, lest the good Governor get any funny ideas.
Possibly, that kinda works for me actually. Still… I think there should had been a defined point in RO where you see the dynamic between Vader and Tarkin form. They never had contact with each other in this film, so it just seems kinda sudden when they reappear in that Imperial meeting in ANH; I get the impression Tarkin and Vader have some kind of history in that scene, but I don’t get that feeling anymore from RO.