By avoiding double transformation. Te only thing you have to do is make sure you dont bind some geometry 2 times over with 2 laticces. So if something is bound by a latice than dont bind it to your new latice.
By just not caring about the latices, the base latices will thn be out of sync but it does work. <- this is atleast whet they are partially doing.
PS: the end result fo the rig is cool, but the rig itself is not in my mind anything special, tough the special may be i what i dont see.