So the official companion guide talks about this, but not too much. Essentially, the likelihood of you getting a new villager in the campsite is based on how long it has been since you've had a villager at the campsite. There is no way you can get a villager in the campsite the day after (or the day after that) someone was in the tent. On the third day after there's a 5% chance, the next day there's a 10% chance, the next day there's a 15% chance, and every day after that there is a 20% chance. From reports of individuals on this forum, the types of villagers you get are skewed toward types that you do not have on your island, or are at least underrepresented on your island. However, I have 5 normal villagers and no snooty or cranky villagers... and I had a peppy in my campsite. So evidently it is not always a personality type you need.