Ages are based on the official documentation you provide - the passports or if allowed, the drivers license and certified birth certificate. When you check in for the cruise they verify the information. Cruise cards are marked to identify the age of the person when it comes to drinking age. You may not realize it, but they are. It is done by the printed codes on the card, or sometimes by holes being punched in the card.
However, if the person turns of legal age during the cruise you can go to guest relations and see if they'll update the person's status.