A small amount of rotational play in the locked cylinder is normal, whether or not the trigger is pulled. The fit of the lock in the notch, and the lock in the frame will allow for a couple of thousandths play, which is easily noticeable. That play keeps the bullet from exerting excessive lateral force on the lock and hand as it enters the forcing cone.
By design, the hand does not press on the cylinder once lockup is achieved. Colt revolvers are different, because pressing on the trigger exerts upward force on the hand, pressing the cylinder to one side of the lock. It is no coincidence that Colt revolvers require more frequent (and skilled) tune-ups.
The most important thing with a S&W revolver is that lockup occurs before the hammer drops in DA mode, and before the hammer is fully cocked in SA. This should be tested using your thumb and fingers to resist rotation of the cylinder while slowly cocking the (empty) revolver or pulling the trigger.
The revolver is more forgiving in normal operation (cylinder not restricted), because inertia will usually carry the cylinder into lockup even if the mechanism is not properly timed.