Yup its per unit, meaning every unit (except vehicles) get to do it. And it's every time they shoot or fight, meaning in the shooting phase it could be: normal shooting > use it, allowed to shoot again for some reason?> use it. Fight phase: normal fighting > use it, using stratagem to fight again > use it. Getting killed and trigger the ancients ability > use it again, shooting overwatch against a unit > use it again, that unit failed its charge and now you get overwatch against another unit? > use it again.
And so on