As far as the state taxes is concerned, yes, the same rule does apply. NY is allowed to tax all of your income as a resident of NY. PA will tax all of your income earned in PA, and NY will apply a credit for the income tax you pay to PA for the income you earn there. I cannot comment on whether the postal service is obligated to withhold NY tax, but you are correct in ensuring the consequences, because you are still responsible for the final result.
For argument's sake, let's assume that your NY tax liability is greater than your PA liability. In that case, although NY provides you a credit for what your PA tax liability is (withholdings plus additional owed or minus PA refund), you still will owe NY the difference. If that difference is large enough, you could owe underpayment penalties. If this is the first time that you owe, there is a good chance that you can request NY to waive the penalty. However, if the postal service cannot withhold the difference for NY, you will want to begin making quarterly (estimated) payments to close the gap.
The following website provides additonal information: Who must make estimated tax payments? (NY). (Wages, while not listed on this site, do qualify as qualifying taxable income. Withholdings towards PA that are credited towards NY should count as if they were withheld to NY). You will be safe from penalties if you owe less than $300 after reconciling your tax return. If you find out that you should make estimated payments, NY allows you to do so at this website: Making NY Estimated Payments
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