Instructor B is correct, but the Plate Umpire on a fly ball will mirror R1. As soon as the ball drops for a base hit, the PU should communicate, "I've got third if he comes."
If the ball is caught, the BU should glance over his right shoulder after all the requirements of the catch are completed and look to see if R1 tagged up properly (if he does tag). If the R1 does tag, then the BU will take the play into second base.