There is no change in evidence: "phaser crews" were part and parcel of the show from the very beginning, drilled to exhaustion in "The Corbomite Maneuver", yet Sulu always was the man pressing the buttons.
How much of a delay was there between Sulu's keypress and the beams emerging in general? We never saw the action in a single shot (say, from behind Sulu's shoulder so that when he presses the button, beams are seen on the viewscreen). We only saw the keypress shot, and then a cut to a separate VFX shot of the, well, shot. There could always have been quite a bit of delay there, due to the men-in-the-loop belowdecks.
Timo Saloniemi