Let’s look at Frank’s backhand volley from start to finish. He hits his split step, pivots with his outside foot and turns his shoulders sideways. As he turns sideways, he gets his tennis racket into position by getting his hitting hand is between his shoulders and the tennis racket angled back behind him. This position looks very similar to the preparation for a slice backhand, but he does not take his racket back as far. His racket and arm position looks like a U or a V-shape (depending on how much of the arm you are factoring into this equation). From this position, at 0:35 in the video, his preparation is done and he is ready to swing forward.
He swings forward by stepping into the tennis court with his inside foot and at the same time driving the racket and his arm together as a unit from the shoulder to his contact point. Remember that on the backhand volley, there is a larger downward component to the swing than on a forehand volley. He makes contact with the tennis ball out in front of his body, and after contact he has a very short follow through to complete his backhand volley motion.