Here in Jackson, MS when I visit a church, the host musician pretty much knows who I am and what church I play for and I ALWAYS let them know that when choirs are changing out to STAY PUT until my choir director is ready (in which case now, it's me.) As soon as that transition takes place, then I take over, to make sure that there is no dead space. (Plus, since I am the only organ/keyboard player at my church, if I'm at a church that has one musician, I'll just go to the other instrument to allow that musician to play with us. I don't have no problem with other musicians playing with us.)
When I'm home, I play until the musician taps me on my shoulder, from there, I ask what key is his/her first song is in, then I transition to it, and hold a certain note, until they take over. The transition is very smooth and some people don't even realize musicians were switched.