I would guess ADR window will open at the same time window as all other ADRs -- online at 6:00am EST, or by phone at 7:00am EST. I think Disney is trying to make this a uniform system, so I don't see them opening the window up randomly at a different time. I would bet go time will be when the entire ADR system opens for a new day.
That being said, I think it's going to be nuts the first 1-2 days. I expect impossible phone lines and website crashes. I went through both several times when this restaurant rolled out -- first, trying to get an AP preview before it was open to the public, and second, trying to get an ADR on the first day public ADRs opened for dinner.