No, you will not have to pay tax on double your NYC wages in NJ. Just make sure that you check the box to remove your NY wages when working on your NJ resident state income tax return. (See Screenshot)
Also make sure that you work on your NY nonresident state income tax return first. This way you will be able to take a tax credit on your NJ resident state income tax return for any NY nonresident state income taxes that you paid on income that is also being taxed in NJ.
Here
is additional information about filing in multiple states (select "see
more answer" to view the entire attachment)
https://ttlc.intuit.com/replies/3300797
