I don't think Tarkin is Vader's boss. Lucas seems to have done a strange re-interpretation of his own movies lately, whereby he thinks that Vader is forced to play a sort of pathetic subordinate role, but that comes from viewing it through the lens of the prequels where he's supposedly been 'degraded' and can't live up to his potential. In the intention of the original films I don't see it that way at all—far from 'taking orders' from Tarkin, they're both important enough so as to be on approximately equal footing.

Just listen when Tarkin tells him to stop strangling the guy: I'm sure I'm not imagining the indifferent shrug in Vader's voice when he agrees. That's not the tone of someone obeying a superior, it's acquiescence to the request of a colleague. It makes no difference whether he lived or died; he just had to be taught a lesson. Notice too that Tarkin didn't intercede until it seemed that things were starting to go too far: if he were really completely in charge, he wouldn't have let it go on as long as he did.