I know what Stevep means and have seen people do the exercise this way but I disagree this is how the exercise was intended to be done. Here is the wording from The Encyclopedia of Modern Bodybuilding:
"Purpose of Exercise: TO DEVELOP THE FRONT HEAD OF THE DELTOIDS. This is the very best deltoid exercise I know, and I always include it in my shoulder routine. By using dumbbells in this manner-lowering them well down in front you get a tremendous range of motion. Execution: (1) In a standing position, elbows at sides, grasp two dumbbells and raise them to your shoulders, palms turned toward you. (2) In one smooth motion, press the weights up overhead-not quite to the point where they are locked out-and at the same time rotate your hands, thumbs turning inward, so that your palms face forward at the top of the movement. (3) Hold here for a moment, then reverse the movement, lowering the weights and rotating your hands back to the starting position. Don't get so concerned with pressing the weight overhead that you begin to sway and cheat; this movement should be done strictly, keeping the dumbbells fully under control. By not locking the arms out when you press the weight overhead, you keep the stress on the deltoids the whole time. This exercise is half Lateral Raise and half Dumbbell Press, and works both the anterior and medial heads of the deltoids thoroughly."
This suggest it is a single movement push and rotating at the same time.