I have suspected this has been the case for a while but never paid enough attention to check if I was right. But since I have a vacation coming up soon, I've been paying close attention to the league schedules in all my leagues. And I finally saw exactly what's happening...and got screen shots!
The shot on the left is from the day before the CUST-35 draft started. You can see that the next sim processed will be FA 5. The shot on the left is from after FA 5 processed and the draft has "started" (i.e. the exact times of picks is now listed).
In the first shot, Late FA 1 is listed as 7/20. But in the second, it's 7/18 and everything after is shifted two days earlier, as well.