If you work in New York and live in NJ, how do NJ state taxes work?

I know if you work in NY and live in NJ, you still need to file taxes. However, can you actually be double-taxed? For example, can one actually OWE taxes in a state they do NOT work in? I’m only asking because my gf’s accountant is telling her she owes a lot of income tax for NJ state, even though she doesn’t even WORK in NJ. I’m questioning this. Any feedback is appreciated.