Don't quote me on this, but I think the issue has to do with time zones. I'm in Chicago so I'll use that as an example...
If I'm eligible to shop at 12:01 AM Eastern on Wednesday, that's ACTUALLY 11:01 PM Central on Tuesday. So, if I were shopping online right when it opens I'd have to use double points day #1 on Tuesday (for one hour) and double points day #2 on Wednesday when I went in-store. If I wanted to only use one double points day, I'd have to wait an hour once the online window opened (aka 1:01 AM Eastern Wednesday = 12:01 AM Central Wednesday) and then I would have double points for the rest of Wednesday use.
If you're already located in the Eastern time zone, then you don't have to do any such calculations!
If anyone has information to either confirm or contradict what I said, please let me know so I can adjust accordingly!