Back when the attraction was being concieved, there were a number of other bands considered, including U2, The Dave Matthews Band, The Red Hot Chili Peppers, and yes, those 3 brothers known as Hanson.
Disney thought the latter would appeal to the teen set they were targeting that would otherwise be heading to Universal's new Island's of Adventure.
However, Aerosmith proved to be a good fit. With the change of the name from "Rock 'n Roller Coaster" to "Rock 'n Roller Coaster starring Aerosmith," the band gave Disney a favorable deal that allowed use of the songs as promotional, so no performance fees would need to be paid.