I understand the limitations of not having a camera etc,, I guess you will just have to LOOK LOOK LOOK a bit more carefully
Pulling back your arm as if to punch: this is why I said in my post, this is purely to display a hitters right shoulder movement, not arm movement... So forget where the hands are in that example and check out what your right shoulder is doing.
Check out Yoda's right arm holies and polies video the main site to get and good idea of what the arms (specifically the right arm) should be doing around the release interval.
With your question, initially the crossline hip slide takes up the slack in the shoulder girdles, it is not a dramatic slide. The right shoulder then drives until the elbow is back on plane and the hands are at about release height, the right arm absorbs the thrust of the right shoulder and the right arm continues this drive right on through the ball.