My SO has that problem, but I never encountered it myself.
It seems that Nook, when someone moves out, will auto fill the spot left with a random villager, and that in usually 2-3 days, sometimes even the day straight after the villager has left.
That makes her mad because she wants to find the perfect villager, but gets stuck with a random villager before she could do a good amount of mystery islands to find it.
So is there a way to tell Nook to not auto sell the spot? (Or is there something that she does that it 'auto sells' the spot or at least looks like that)