Mirage Island....
There's something in the FAQ about that. The RS FAQ.
Everytime you catch a Pokemon, a number is given to it. And everyday, a random nmber that makes Mirage Island show up is picked. If one of your Pokemon's numbers match that picked number, you get to go to Mirage Island.
Either way, you can't seem to be able to see the "numbers". Hidden factor in the game, I guess.
Talking to the old guy in Pacifidlog Town just tells you if you have a such a Pokemon or not. You don't have to talk to him.