NY starts with your Federal AGI which is found on line 19 of the IT-203 then they make a few adjustments, but they calculate the tax on your entire income, then on line 45 they use your NY income amount divided by your federal amount and apply that percentage to your calculated tax. So, although it appears as though they are taxing all of your income, they really are not.
Also, keep in mind that NY income tax rate is a graduated system and is higher than the PA income tax rate. So, even if you only won $5,000 in NY, but had an overall income of $100,000, your tax rate if you are single would be 6.57% as opposed to PA 3.07%.
https://www.tax.ny.gov/pdf/current_forms/it/it203.pdf
https://www.tax.ny.gov/pdf/current_forms/it/it201i.pdf#page=57
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