Blackout period start when you leave, not join
I understand the reason for having a blackout period, which is to prevent abuse of game mechanics by hoppers, and I agree with the concept. But the way it is currently implemented also affects people that are not hoppers.
For example, I was getting a bit burned out from doing the Expert Map55553/High Tier AW grind with my former alliance. I would have been happy to stay with the group and go to a more casual play, but with a 30 member cap and everyone needing to participate to 100% 3 groups each day, obviously that wouldn't work. So I stepped aside to let a fresh body in, and I went solo for a few months.
Eventually, I got bored just grinding arena milestones, so I looked up people from my 1st alliance, saw them in a more casual alliance doing Advanced Map24242/Lower Tier AW, so I joined up with them recently, and naturally the blackout period started. As this most recent AQ series ended, naturally I didn't qualify for rank rewards, despite the fact that I was not what people would call a hopper and I easily did my fair share of the work in all 5 days of the AQ.
And that seems a little wrong.
TL:DR = Currently the blackout period starts when you JOIN an alliance. My suggestion is that it starts when you LEAVE an alliance.