No, they won't tax your Illinois income. However, NY will pretend that all of your income is taxed in New York, and then prorate the tax to the percentage of income being earned in New York. Your Illinois income is factored in to determine NY tax, but is not taxed in NY.
Having said this, please comment if your W-2 has all of your income as NY wages. There are two possibilities if that is the case.
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