The only real way to know is to keep track of all the villagers that left. They should show up on mainstreet and disappear once you've cycled enough past them. I am not sure how "certain" it is, but I believe most people have seen them show and leave accordingly.
They will not remember you when you invite them to your town again.
As for how they show up. The easiest way to get them back is to find someone selling or giving them away. The chances of them showing up in your campsite are slim, but possible I suppose.
They won't just move in either unless you have 8 or less villager and you reset for that villager if you don't already have that personality in your town.