Here is a video of a conducting ping pong ball transferring charge between two conducting plates with high voltage (~100,000 volts) on them.
Once the conducting ping pong ball touches a plate, the ball and the plate are at the same potential, and the electric field lines from the other plate terminate on the conducting ping pong ball. Because the field lines terminate on the ball, the ball has charge on it (Gauss's Law). Because this charge is the same sign as the charge on the plate it is touching, it gets repelled by that plate and attracted to the other. When the ball hits the other plate, it deposits its charge, and gets charged by the other plate.
So the charge transfer is due to electric field lines transferring from the plate to the ball when the ball makes contact with the plate. Charge migrates to wherever the electric field lines terminate on the ball.
Look at another way. When an uncharged conducting ball is in an electric field, it has a dipole charge on it, + charge on one end, and - charge on the other. When the ball approaches a plate with + charge on it, the - end of the ball is closest to the plate. When it touches the plate, both the ball and the plate are at the same potential, so the - charge on the closest end of the ball transfers to the plate, leaving only the + charge on the other end.
I hope this helps.
Bob S