Eager Partner?

[BlitzkriegBob]

From a Fed game last week where I am PU. Partner is pretty good, no real problems with him (first time working together). First occasion, lead runner coming in to 3B (trailing BR still on bases), I am down the line getting in to position with a throw coming in. I see BU coming over so I verbalize "I got third" (loud enough to make the 3B coach turn towards me), but BU continues to move in. Luckily ball gets away so there's no call to make. Second occasion, we have a rundown between 2B and 3B. I am in position to take the lead, but BU is right smack dab in the middle, so I verbalize "I got this end" (again loud enough to make the 3B coach turn). There is a series of quick throws as the BU does his imitation of one of those target ducks that twirls back and forth before the tag is made as the runner is retreating to 2B and BU rings her up.

My questions is this: After letting the BU know that I am there to make my call and he is still right there to also make the call, what should I do? In both cases, I was thinking to myself that I was going to let him make the call (and the rundown did turn out to be his call) in order to save us from the possible double call, but what should I have done?

He was a 20-year veteran and after the game he was more concerned with fraternizing with the coaches than reviewing game so we didn't get to discuss the coverages. I know we pre-gamed, but I don't remember for sure if we went over these situations. More than likely we didn't.