I was obsessed with this feature for a good week and all I did was amie
I tried using all dragon pokemon to see if I could get dragon items but nothing changed
You can get them from passerby too though and I think those are the ones that can actually get you items related to the pokemon
I played around with this so much that I actually have an item that isn't listed on serebii
Poison smoke object
If you put down a pokepuff in the house new passerby will appear in the amie house and three fire pokes can you get you a heat rock cushion and if you get three flyers alot of the time you get a flag perch.