Thank you! TurboTax ended up doing it all for me and telling me that I owed state income tax (which made sense to me after some research).
For anyone else confused: This state doesn't require state income tax to be paid if you make under $600 as a nonres. I'm guessing my previous employer mistakenly didn't report it because we visited the state on two separate occasions which totaled under $600 each time (but definitely over $600 in total). That or they did end up correctly withholding and the W-2 is just wrong. I'll check with my employer to see if they already withheld state income tax but to avoid any trouble with that state, I went ahead and paid what is believed to be owed.
