No, your resident state has a right to tax your income, no matter where it is earned.
In your example, Delaware would tax the income you earned there. Pennsylvania, as your resident state, would also tax this income, but you will receive a credit on your resident Pennsylvania return for the tax you paid to Delaware on this same income. This avoids double-taxation. It is important to complete your nonresident state first so the credit for taxes paid can correctly calculate on your resident state's return.
The examples they were talking about above had to do with part-year residency. In that case, PA would only tax the income you earned while you were a resident there, or if you had PA-sourced income after you moved out of PA.
@ycchan
