You're not missing anything, but you are misreading the New York tax return. New York is not taxing all of the income, but it does use all of your income to calculate how much tax you would pay on all of your income. Then, the tax is prorated to the amount of income that is New York income. What you should be seeing is on the New York tax summary, it will list all of the income as "taxable" in New York, but your actual tax will be based on the income that is actually attributable to New York, and this will show up on the IT-203 as well.
Thus, on the New Jersey return, you will get a credit for the amount of tax you pay to New York on this "double-taxed" income. It will not be the full amount that you paid to New York. Rather, it will be the amount of tax that New Jersey will tax on the same income. And remember that New Jersey does not tax unemployment. So it's likely that you will not have a tax credit for New York on that portion of income for that reason.
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