I think what knightofdragon said is right - They can only be born with Pokerus if they had it as an egg. Pokerus spreads to an egg just like to a regular Pokemon - Having a Pokemon with Pokerus in your party, or battling one with Pokerus.
That means one of your Pokemon had to have Pokerus, because eggs can't get it by battling. If you ever battled with Igglybuff, which I don't think you did, it probably got it from a wild Pokemon. The only other way is a glitch. The Safari Zone has nothing to do with it. :P
As for your other question, you don't have to take Igglybuff to the Pokemon Center for Pokerus to take effect and double all EVs.
Hope I helped :)