If they do not, it has not been applied this turn. Example: Zilean, Time mage reads “Once each turn, if you would play a token unit while I'm at a battlefield, you may play that token and an additional copy of it instead.” When his controller plays a token, they can choose not to apply the replacement effect to that event. If they do, they can choose to apply it to a later event of a token being played.
§ 371.2.b Core Rules PDF (officieel)
§ 371 Some Replacement Effects will begin with “once each turn,” or “N times each turn.”
§ 371.2 If the Replacement Effect says a player “may” apply the Replacement Effect, the player has the choice of whether or not to apply it.