Understanding of SPACE in non deterministic Turing Machines
A nondeterministic Turing machine is a Turing machine that has a "guessing" mechanism. It accepts an input if there is a sequences of guesses that leads it to an accepting state. It rejects an input if all guesses lead it to a rejecting state.

The time complexity and space complexity of the Turing machine are defined in exactly the same way as for deterministic Turing machines:


The time complexity on inputs of size $n$ is the maximum number of steps that the machine executes before halting over all inputs of size $n$ and all guesses.
The space complexity on inputs of size $n$ is the maximum number of tape cells that the machine uses over all inputs of size $n$ and all guesses.


If your machine always uses only a polynomial amount of space, then it is is NPSPACE. Note that NPSPACE=PSPACE, a consequence of Savitch's theorem, and so you can convert it to a deterministic machine using polynomial space (the amount of space used could increase).