The only thing I found online about this is the following blog: http://blog.computationalcomplexity.org/2005/03/tape-reduction.html
where they write:
Roughly the simulation guesses every step of the transition function on one tape and uses the other tape to verify the transition function on each tape of the original machine one tape at a time.
How exactly do you guess the transition function? And if you guess it, then why do you need to verify it? Isn't the guess in non deterministic turing machines always correct?