Yes, you are a NY non resident.
This means you will file your NY nonresident return first, then claim a credit for the taxes paid to NY on the income that is double reported on your NJ return.
You may or may not still end up owing money to your resident state depending on whether or not their tax rate is higher or lower than your nonresident state. If the non resident state had a higher tax rate than your resident state, your credit will be limited to the amount of tax you would have paid to your resident state. They will not give you a refund of the taxes you paid to the nonresident state.
Multiple States
File Non Resident State Return
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