It's not "counting" your entire income. The first page of New York Form IT-203 has two columns for income. The first column is federal amounts, and the second column is New York amounts. The federal amounts on lines 1 through 19 should be the same as on your federal tax return, and include all your income. The New York column should include only your New York income.
The way New York calculates the tax, it first calculates tax on your entire federal income, after New York adjustments. But then it applies an "income percentage" that is your New York income as a percentage of your total income. That's how it adjusts the tax based on how much of your income is taxable by New York. You can see this on page 3 of Form IT-203, on lines 45 and 46.
