Yes, when approaching Tag-Outs it can be helpful for the sake of focused heightening to only tag-out one side of the scene – keeping one character consistent and heightening his/her Personal Game. And yes, when choosing between two players to tag-out it is often advantageous if you replace the catalyst and keep the character reacting to that catalyst.
But there are no “rules” in improv, just tools and considerations.
Sometimes what feels “right” in the moment goes against a standard guideline. The game below is one of those times.