So to pass the class change to all players you have some options, but start with all your class selectors disabled, or Enabled During Phase None.
Use the RNG connected triggers to enable the desired class selector
If your doing the random class more than once a game, use some event to disable all the class selectors before next random class selection.
Use the Change Player To Class Function, with an event that can get at all players.
Like maybe use a second trigger, to enable a mutator zone, which then gives out the On Player Entering Zone event.
Add this event to all the class selectors and only the RNG enabled class selctor will work.
If the area is not too big when class change happens, you could also use the class selectors zone to change players, instead of by function.
If players are all over the place and not easily zoned, you could also use player reference devices registered to each player and use their on activated events to change class.