The unofficial answer to this is "when they are ready." The stated boarding time began at 12:30, this was recently changed to 11:45. However, even with the later boarding, we had times when they started boarding well before noon.
It depends in part on how long it took customs to "clear" the ship from the previous cruise and to get people off. Stateroom stewards start cleaning the rooms as soon as people leave them to go to breakfast. As soon as things are taken off, the new supplies, etc. for the next cruise are loaded on. I don't really know what HAS to be done before they allow boarding, but we've had as much as an hour variation between the earliest start of boarding and the latest (we've done 9 Magic cruises). What I can say is that it is usually a bit earlier than the "announced" time.
With the earlier boarding time, it is common that your stateroom is not ready at the time you board. You are told that the rooms will be ready at 1:30. We were able to go to our room and drop our carry on bags. Our steward was a little concerned and asked us not to leave anything of value as he wanted to be able to prop doors open to make his job easier. I guess my DD considered her AG doll "valuable," but her "sister" didn't need to go to lunch with us!
With the earlier boarding, you get on the ship, then go to lunch (Topsiders or Parrot Cay.) You can then request dining changes, register for the kid programs, make spa/Palo reservations, etc. Do the Spa/Palo FIRST!!! Then Flounder's, then whatever else.... Then go up to the pools....they are empty on embarkation day. You really have plenty of time before the safety drill.
No matter what the stated time, you know that it is time to board when they open the doors!!!