Things seem a little broken right now - there was some kind of update earlier this week where a bunch of availability was dumped all at once, and then nothing.
For regular dining reservations, they in theory drop at 6am pacific. For special packages like WoC dessert party, those have been dropping sometime - not super consistent, but in general between 1 and 3am. Unfortunately there is not a lot of consistency again - after several months of it, I had thought DLR had finally fixed its dining res issues, but it is back to a guessing game now.