Things will not straighten out automatically with the filing of the Delaware return. If you have a W-2 with Pennsylvania and Philadelphia tax withheld, it means those payments were sent to Harrisburg and Philadelphia. Usually the employer can't get those back. You'll have to file a PA tax return and possibly a Philly wage refund petition.
I don't quite understand your situation. Do both your W-2s show your total federal income and different state amounts (one for DE and one for PA)? Or are they split? For example, do both W-2s show $1,000 in federal income and ~$1,000 in state/city income or do you have $500 on one and $500 on the other?
If your W-2s have duplicate federal wages, you can file a nonresident PA return and put down $0 wages to get your PA withholding back. Submit a legible photocopy of your two Form W-2s, and a SIGNED COPY of the Delaware return that you filed/will file (without the supporting forms and schedules), and a statement explaining the U.S. Census made a mistake.
If your wages are split, you can do the same, but you should verify that you are reporting all your Census income on the DE return.
For Philadelphia, the Census can file a mass refund petition if this is a big problem, but you will probably have to file an individual wage refund petition. This has to be signed by your employer (the Census).
2020 Wage Tax refund petition (salaried employees)
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