As others have said, it's usually not really necessary to make DLR ADRs right on the 60-day mark. The new day rolls somewhere between midnight and 6:00 am, but it doesn't seem as consistent as WDW.
One thing to note, the system has been having issues of late. DLR hasn't been consistently loading reservation times, especially for park opening meal times and dining packages, on the 60-day mark. So, if you do check for the BB F! dining package right on your 60-day mark and it's now showing any available times, it most likely means they haven't been loaded into the system yet. You'll have to keep checking; it could be loaded that day, in a few days, or not for a few weeks.