That could help explain it, but did they ever confirm that time passes at a different rate in the alternate worlds or just in between worlds? I remember the crew went 'back in time' relative to SS when they transitioned but when they came back I assume they went 'forward in time' relative to SS and it balanced out that the week or so they spent in SS was a week or so in the human world. It was still the same summer they left, with only a little while before school started up again when they came back to the real world. The time discrepancies might work both ways, or it could just be a plot device to make the characters more interesting. In the end I don't read Bleach for the properties of the world it takes place in.

As to the Privaron Espada though, I have always been under the impression that Arrancar can be born naturally and Aizen had just been working with the naturally occurring ones for a while. The Hogyoku seems to be a catalyst for the Arrancar transformation helping to ensure it occurs as smoothly and completely as possible, but I think the Privaron's, and probably even some of the current Espada came to be naturally even before Aizen even started working with Hollows.