In my experience, amiibo villagers are very permanent in New Leaf. I've heard if you have enough amiibo villagers in your town at once, they'll start moving out like normal villagers, but once their number goes under whatever the threshold is, they'll stop asking to move out.
That said, I believe you can force an amiibo villager to move out with another amiibo. But I haven't actually tried it myself, so I'm not 100% sure.