Show up at the RAC counter the day you are leaving--within the time limits as posted. I think you need to be at RAC at least several hours before your flight and since they open (I seem to recall) at 5:00 AM, very early flights using RAC would be questionable at best.
Should add that RAC is not operated by Disney at all, but by a private company. They won't know a thing about you or your flight until you check in at their counter.