Let’s look at Frank’s forehand 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 lays his wrist back so that his hitting hand is between his shoulders, but the tennis racket is angled back. Remember that from the front, this racket and arm position looks like a U. From this position, at 0:30 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 he swings forward to his contact point by driving the racket and his arm together as a unit from the shoulder. 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 forehand volley motion.