You should be paying taxes to Delaware. If you worked in Delaware, your employer should have withheld taxes to Delaware. Delaware and Virginia do not have a reciprocal agreement. Delaware doesn't have reciprocal agreements with any state, in fact. That means when people work in DE, they need to pay taxes to DE.(unless, perhaps, you are in the military or your spouse is in the military)?
You get a credit on your Virginia return for the taxes you pay to Delaware. This reduces double taxation. The taxes you pay to Delaware are based on your Delaware tax return, and the tax liability on it. You couldn't get a credit on VA for paying $0 to another state.
Why didn't your employer withholding Delaware taxes?
