Letting Pokemon amie going on while you go about your normal game, up to 3 Pokemons from your contact-friends will eventually sit down and confer together and leave you a gift. ON your birthday, you'll receive 3 supreme wish pokepuffs. Also, be aware that the first pokepuff you have on your 'feeding roster' will replicate in your friends's games. As I play on 2 games and game consoles at the same time, I was able to notice that.
However, I have no clue what the dialogue between the 3 visiting Pokemon do refer about...
