Amiibo Card invited villagers may ask to move?

[Buster Bunny]

So I decided to use my Caroline card to make Muffy move out from Acme since she never asked to leave.

It's possible for Amiibo Card invited villagers to leave after a certain time?

 

[Licorice]

I'd imagine so otherwise people couldn't cycle them/sell them.

 

[Moonfish]

People say it's possible for them to move on their own but for me it's only happened when my entire village is from cards, then when some "natural" move ins happen the amiibo villagers never ping again.