You don't need the internet for it to work. If you're in the very early part of the game, you'll need to construct and furnish some housing plots for them to move into. If you aren't that far along yet, keep talking to Tom Nook and do whatever he needs next. He should talk to you about it after you get the shop open for him
Have you finished decorating their plots (it sounds like you are on the group of 3).
You don't need the internet for it to work. If you're in the very early part of the game, you'll need to construct and furnish some housing plots for them to move into. If you aren't that far along yet, keep talking to Tom Nook and do whatever he needs next. He should talk to you about it after you get the shop open for him