You are incorrect, New York taxes all income earned even in other states, so your full salary would be listed as New York income. To compensate you for earning income in other states, when you calculate your New York tax, the rate of tax will be reduced by the proportion of your income earned in other states. So, you will report your total income to New York, but only are taxed on a fraction of it.
When you prepare your New Jersey return, look for a credit for taxes paid to another state to reduce your New Jersey tax by the taxes paid to New York.
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