How is the concurrent tracking of "state position" in NFA's typically modelled?
The theoretical treatment is just to say "It's what happens: that's what nondeterminism is." The machine accepts if there's any computational path that finishes in an accepting state.

Anything about memory, caches or concurrency is a matter of implementation.  The simplest implementation is to keep a vector of Booleans that records whether or not the machine "could be" in each of the states at the current step of the computation.