NintenDan reports that the fast-time list is unlike that in the first two games of the Advance series.
In those games, it's one chart per CHARACTER per level.
In Sv3, there is just one chart per level, regardless of character.
As such, until further notice, tracking will take place much the same way as it does for Knuckles' Chaotix: the best single time with any combination of characters will count. Figuring out the best team to use in each level is your own job.