I would call when I am at the exit door, as you do speak to the driver, so he knows exactly where you are and what you are wearing...to pick you up.
I would give him the further destination but it doesnt matter. Either way you dont need your phone with you to complete the payment, so the phone can get out before the ride is over.
-1 In my experience, when I do that, they get confused when you give a new (first) destination. Instead, give the first stop so that they can get going as soon as you get in, and on the way, go into the app and change the destination. The driver will get your updated destination, but after the first one is already in his GPS.