How Does Asking Villagers to Move in Work When You Have 10 Plots Already?

[yukimin]

Little confused about this. Let's say I have a full town of 10 villagers. If one villager asks to move out, should I be visiting other people's towns/Nook islands to ask new villagers to move in when the old villager is in boxes? The day after the old villager moves out? If either of these, is there only a one day "window" to ask for new villagers?

 

[maarowak]

Also wondering about this!
I already messed up inviting my amiibo villagers with the new plots (sob), so now I need to wait everyone to move out, but I don’t want to mess up again!!