you're welcome, i know it can be hard to get a handle on for a little while when you're first starting! D:
even though you hit the power button, the game still loaded to that date, so it wouldn't have mattered anyway, unfortunately. but yes, as long as you got the confirmation from him that was moving in, he will absolutely move in no matter what. the only thing i can constantly stress is to never break your cycle, even if you think you should; just keep cycling, and the villager will show up. now that you've dropped to 8 villagers, you'll need to TT day by day until someone new moves in, and then keep TT'ing day by day until someone goes into boxes again. from there, you're free to cycle again.
from now on, don't TT to any date besides your three! say your boxes day becomes august 30th, 2016 -- you should only ever be TT'ing to august 25, 2015 > august 25, 2016 > august 30, 2016. no exceptions, unless you need to change your boxes day or aren't cycling anymore. trust me, as long as you stick to that, you won't run into any more problems! (or you're way less likely too, lol!)