Dear bgolfing,
If the putter moves itself and the timing is right, that's great. If the muscles move the putter with the right timing, that's also great.
Once you learn the timing of a "one potato" backstroke and the timing of a casual relaxing of the shoulders and arms and putter from the top of the backstroke to the bottom of the stroke, the timing is all that matters. The backstroke is a blast-off from the bottom at address so that the stroke lasts "one potato" as it coasts to a stop at the top of the backstroke right on the "to" syllable (not before or after) and the downstroke to impact always takes one-half of the time for the backstroke with a steady, smooth acceleration from zero at the top to a peak speed at the bottom. If the timing is right going back and coming down and the accleration is smooth and steady, then the velocity of the putter head at impact will be just right to roll the ball all the way and not past the target distance. This timing pattern (backstroke, downstroke, acceleration rate the same and smooth) is what allows the instincts to select the right size of the backstroke (and thus the right impact velocity at the bottom) thru the "blast-off and then coast to a stop" backstroke.
The smoothness back and thru means that the hands are in sync with the handle and the shoulders are in sync with the putter head and thus eveything between the shoulders and the putter head are also in sync and unchanging. This "feels" in the hands on the handle like nothing changes during the stroke. If you feel something abrupt in the stroke, then the timing is off (almost always too fast).
The shoulders put the hands back and up, the putter head back and up, and the arms back and up. Relaxing from the top of the backstroke allows all of this meat and metal to drop wherever gravity wants to take it. The whole falls down and swings beneath the pivot at the base of the neck, bottoms out right beneath the neck, and then the putter head rises into the back of the ball as the neck stays still (and does not follow the putter head to the left (right-hander)). The dropping / swinging under of the arms and hands and putter does not get timing from the heaviness of the arms etc., but simply from the length of the whole from neck to end of putter (or at worst from neck to hands, with the putter getting brought down by this basic neck-to-hands pendulum). The putter is quite a bit lighter than the arms and hands, so a stroke with a putter in the hands and a stroke without a putter in the hands both look very similar in timing.
I hope this helps.
Geoff Mangum
Putting Theorist and Coach
PuttingZone.com
http://puttingzone.com