Each shooter activates a pressure sensitive switch when he's got a clear shot, that illuminates a green light on a control panel; each shooter is poised to take the shot while he's indicating green. You then have a team leader that is in charge of giving the shoot order. When all shots indicators are green, he gives the order: "shoot". All shooters fire at the same time.
Put all those switches in series (or into an AND gate) and the light or buzzer doesn't come on until all three buttons are pushed simultaneously. They don't need a spotter to tell them when to fire, that only creates a delay.
(I dunno if that's how they did it, but it would be plausible and cheap to implement)