With Charlie we closed at 1:00pm the day of (the hurricane hit about 8:00pm at night.) Charlie was kind of a funny story:
Initially Orlando was supposed to be safe, just get the outer edge of it. In fact, everybody from Tampa was evacuated to Orlando. The parks were only clsoing early as a precaution. It was in the middle of the day (maybe about 1:00pm) that it was announced Charlie had veered off the expected course and the eye would now pass over Orlando. Thankfully we had already decided to put our Hurricane Plan into place.
It ended up missing Tampa completely (and I-4 was am ess the next day with all the Tampans trying to get the hell out of dodge!) All but DAK opened up the next day. DAK took 3 days to get ready due to habitat destruction.
From what I understand, Disney did not charge the day we closed early and did not charge extra nights for people who were supposed to leave but could not because of the hurricane.