New York uses your total income to determine your tax rate, then applies it to the New York income while you were a resident. New York has a progressive tax system- meaning the higher the income, the higher percentage of tax is applied.
For example, if the NY tax rate is 10% up to $100, 25% for $101 to $250, 50% $251 to $500
If you made $200 total but was only a Part Time NY resident for half the year,using only your NY income ($100) would tax you at 10%- but you made $200 all year so you must pay at the 25% tax rate. It's only "fair".
@sueg615
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