I have invited Zell through Amiibo. They'll ask you to craft something and you can ask them to move in, but they'll say they're not quite sure they can move in before knowing the island better. Hint hint to inviting them again.
On the third day of repeating this, they'll agree to move in and I had Zell the next day.
Yea, you can scan the card once a day and the Amiibo will come over immediately. So do that three days in a row and on the third day, they'll agree to move in, if you ask them. On day 1 and 2, they won't feel prepared for it yet.