Yeah, make sure when Isabelle says that Mr. Tortimer is waiting to see you at the dock, make sure to go down there and talk to him. He'll say that the boat (Kapp'n) will start showing up starting the day after. Good luck
I think you need to upgrade your tent to a house or if not, try to get the second upgrade (not second floor but a bigger space) in order for Tortimer to appear for you to have access to the island.