I think this skill is somewhat similar to Geminate Attack from DotA Allstars.
The hero with this skill attacks twice (very fast, just like one attack) once every X seconds depending on the skill level. If you could just get the code for that skill and modify it to make it attack 4 times instead of 2, your problem is solved.
Anyway, I thought of something, but I'm not sure this will work. Create a custom unit: Unit1, Unit2, Unit3.
Set their Attack Cooldowns to something very low, and their projectile arts and attack damage just like the tower you mentioned. Create a trigger that:
If tower attacks, if this has skill, create unit1 in position of attacking unit, order to attack attacked unit, wait ATTACK COOLDOWN seconds, then remove it. Do the same for each Unit[x]. I think this will make the tower attack (showing the projectile) then before it reaches the target, Unit1 will show and attack, remove, Unit2 will show and attack, remove, and finally Unit3 will show and attack, remove. It will look like the unit was attacked 4 times. Of course, the dummy units should have the locust ability and must have no model.
I don't think it will change targets during the cycle though, and if the tower has a very fast aspd, it can attack another unit while the dummy units attack the other unit.