Well, according to the fluctuating time theory above, FTL (whether that encompasses all of the doors in the hat or just the EF) is one strand of time, and our “real world”, SB, is another strand of time. In the strand of FTL, time fluctuates, but the characters live their times like normal, like we would, even though if an outsider were to enter FTL, they may enter into a time that would me, say, 10 B.C.E. in our world. Because SB is a different strand of time, time works differently, and our time would always progress forward at a steady rate. So, a character could cross over from FTL to SB and age, because in SB, time moves at a normal forward pace. Except, of course, in SB.
I would say this is because the curse specifically stops time. But maybe it doesn’t. Maybe SB is frozen in time just as FTL is (kind of), except that in FTL, the characters retain their memories, and in SB, the characters’ memories disappear (which is what the curse aims to do).