This is from the official sweepstakes rules:
If, on any given day, a location in a Disney Property is randomly selected: a time for awarding of the prize will also be randomly selected. ...Sponsor anticipates that potential winners will be selected at the Disney Properties between opening and 5 pm local time; however, certain prizes (for example, Mickey Mouse Penthouse and Cinderella Castle Suite) are likely to be awarded early in the day to help ensure that a winner will be able to claim the prize and Sponsor reserves the right in its sole discretion to select winners at the Disney Properties during any operating hours.
So unless there is an issue, for example the person declines the castle stay, they can re-issue the prize at anytime, but they anticipate all prizes to be awarded between opening and 5pm... The reason for this is that AK closes at 5pm duriing certain months of the year, so to keep it fair that is the latest that they would want to issue prizes in any of the parks. Also, keep in mind that at WDW prizes can be given out at any of the 4 theme parks (MK, AK, MGM and Epcot) the water parks (Typhoon and Blizzard) and DTD. So prizes like the Castle stay can be awarded at any of these locations, it is not MK exclusive.