Employer incorrectly paid taxes to VA even though I live/work in DC. Is it correct to file a nonresident form to VA? VA refund is much less than what I owe to DC.

I'm very surprised at the difference in my VA refund ($5100) vs. what I owe to DC ($6300), even though the effective tax rate shouldn't be so different. Am I correct in submitting a nonresident form to VA and then a Resident form to DC? Thank you!