I don't know specifically when the system rolls, but it's sometime after midnight, but before 6:00 am. As others have said, you don't need to be online right at the 60-day mark when the ADR window opens, but if you have a specific place you want to eat and a specific time or are going at a super busy time, I would make ADRs sooner opposed to later. That being said, there are a fair number of ADRs still available for Christmas Day dinner and the day after Christmas dinner, which are both pretty busy days in the parks.