Intern in non resident state, but company taxed me based on my home state

Hello,

I am a university student who claims full time residency in that state. I worked a 3 month internship in DC over the summer. However, based on my W-2, my company filed to have my taxed by my resident state. I never paid DC tax, despite living and working there for 3 months.

If I go to file a nonresident return for DC, it asks how much I expect to receive in refund. However, I believe in actuality that I owe money to DC and am owed all the taxes I paid to my full-time residency state, since I never actually worked there. This is despite the fact that TurboTax says "Based on your federal return, you still may need to prepare a return for [RESIDENT STATE]".

Is this correct? Further, is there a way to specify you owe instead of are owed when filling out the non resident return?

Thank you very much for the help!