What is this feature in Pokemon Amie?

Question

In Pokemon Amie, other trainer's Pokemon walk to the centre of the field, and once three gather they start conversing among another, and you receive an item.
What is this? Does it happen automatically or not? If it does, what determines whether the Pokemon stops at the field or not?

Answer 1

This feature is anoher way to get items in Amie, such as Poffins and furniture.

While the player is viewing Pokémon-Amie, Pokémon from recorded Friends, Acquaintances, and Passerby in the Player Search System will visit the player's Pokémon-Amie space. One by one, Pokémon will enter the player's space and decide whether they want to stay for a while or move on. When three Pokémon have decided to stay, they will start a dicussion amongst themselves, and, 30 seconds later, they will leave a gift and depart. These gifts may be Poké Puffs or interior items or wallpapers for the player's Pokémon-Amie space. If the three staying visitors have a common type, the visitors will leave a special gift related to their shared type.

These are the basics of visitors feature in Amie, if you want to know more, here is the source