You have to complete the missions, or you could fly to the second island using the cheat "CHITTYCHITTYBB" on PC. Once on the second island, you can enter the subway tunnel and go to the third island. If you unlock the second island, you will not be able to use the subway tunnel to go to the third one because it will be locked just like the one in Portland
Hope this helps
Oh, i just completed Luigi, Joey and Toni's missions. Only some missions left and im done with the S missions.
Ya, when Sal tells you to pick up a car that's covered in "brains" you will officially unlock the second island. Just do the missions given to you by Luigi, Joey, 8 Ball, and Salvatore. Salvatore's missions will come back eventually despite you being "done" them (S missions)