Tips i have picked out because i have a new town too!
- Once they stop giving you tutorials (they will mention about saving so that is when you know they have stopped)and ask you to do favors people will start moving out
- You have to be the Mayor first
- You have to start talking to the villagers more, building a friend ship because the more friends you are with a villager the more likely they will ask the move out!
Hope that helped ~ (people say you need to unlock the island before anyone moves out, lies! I don't have it and people are moving out still)