I have always recheduled regardless whether it was moved earlier or later.
Never a charge with the exception for one time, they moved my flight for 3minutes and I wanted to move to an earlier flight, they said it should be a charge. I thanked her and hung up without accepting the change. A week later, the same flight was moved again, and this time was to leave 17 minutes ealier. I called and was able to reschedule to a better flight schedule.
Search this board, I don't think anyone has reported charges for flight rescheduled due to the change by Airtran.