From reading about multiboxers and seeing some in game most are not multi tasking as you imagine. Most have a program were a key click activates all the characters in the multibox team. One key click and all the characters cast their major spell in unison. It might take some planning and programming skill to create the system but once created there is very little to no multitasking to play multiple characters.
This is why many multiboxers have multiple versions of the same class. Multiple mages or multiple hunters. One key click and all the mages cast frost bolt. I saw a multiboxer in stv with 3 mages doing just that. One key click and all the hunters have their pet attack. One key click and all the hunters cast arcane shot.
eta: There’s a post on multiboxing on the classic general discussion forum that illustrates how most multiboxers posting have multiple versions of the same class.