When I released the cup, the ball and water all fall together at the same speed, which increases as they continue to fall due to the force of gravity. The cup hits the ground first, then the water slams into the bottom of the cup. As water molecules pile up they collide with each other and create a compression wave that travels upwards very fast, like instantly. The water has much, much more mass than the ping pong ball, so when the upward moving wave collides with the downward moving ball a tremendous amount of energy and momentum is transferred to the ball as you saw in the video. I think my second attempt shot back up over 15 feet in the air.
If your having problems getting the ping pong ball to shoot up, try swirling the glass then put the ping pong ball in the glass. This will keep the ball in the middle of the water.