Going along with 5263's point, it's very very important that you are "stalking" the ball or trying to find the ball with your non-hitting hand. THAT should be done as soon as possible.
More or less, when you find the ball with your non-hitting hand, you automatically initiate your unit turn. Once your hitting hand separates, you want your takeback to be ideally against the direction of your overall momentum. That gives you the smoother, more rhythmic backswing that gives you the better timing.
It's a little like throwing a football while rolling to your right. Unless I'm running at full sprint, I still want to find my target before I separate my non-throwing hand from the football. If I just separate, THEN roll out, that will end up just as a pitch or dink-and-dunk pass.
Directory of Tennis Warehouse Clubs (courtesy of Mountain Ghost)