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Get your taxes done using TurboTax
NY is going to look at your total income to figure your tax rate and apply it to the NY income. In other words, if the NY income alone puts you in the 4% bracket, but your total income would put you in the 7% bracket, NY will charge you 7% tax.
NJ: Since you already filed federal MFJ, you have no choice but to file NJ MFS and declare all your combined worldwide income.
You should have included your spouse's world-wide income on your federal MFJ return. If you did not, that return is wrong and needs to be amended. If you did include your wife's world-wide income, it should automatically flow to the NJ return in Turbotax. (If you are filing manually without software, then yes, you must include all your wife's world-wide income--because you were domiciled in NJ the whole year and you are filing MFJ, she is considered to have been domiciled in NJ the whole year.
NJ should give a credit for the actual NY tax amount. In other words, if your NY withholding was $5000 and your tax is $3500, you will get a $1500 refund from NY, and NJ should give you a credit against the $3500 (the amount of actual tax, not the amount of withholding).