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Coteaz and his unit can make an out-of-sequence shooting attack against enemy units arriving from reserve within 12" and LOS of him. Is his shooting and that of his unit effected by whether they have moved in their previous turn, in the way of preventing fire from "Heavy" type weapons?

No. Remember that they only can't shoot if they have moved during their own turn.

You are only restricted from shooting if you have moved in the preceeding movement phase - which you most likely havent, as that is your opponents movement phase