The turret movement is coded to not trigger "On shoot" unless its within something like 1 degree of the target. This means a machine gun with turret movement isnt going to randomly spray bullets forwards while it rotates to the target - it only shoots AT it.
So yeah, Doppel's on the right lines, make the rotate speed really high and turn off the Sprite's rotation and the Turret will be happy it's pointing at its target.