Can an $NDTM$ simultaneously perform a set of operations on all strings of a given length?

Can an $ NDTM$ perform a set of operations on all strings of a given length $ b$ , at the same time? Aka can it operate on all strings of a given length by doing something like: spawn $ 2^b$ branches then operate on each string of length b on each branch?

How could it do this tho if the branches can’t communicate? That’s what I’m having a hard time with. How does any given branch, if it doesn’t know what strings the other branches are running, know what string to run the operations on (so that all the strings are covered by $ 2^b$ branches)?