Something's wrong, but I can't tell exactly what. You should not have gotten a refund from New York, and you should not have had to pay any significant amount of tax to New Jersey. You should have paid New York tax and gotten a credit on your New Jersey tax return for the tax that you paid to New York.
You should have filed a New York nonresident tax return, Form IT-203, and a New Jersey resident tax return, Form NJ-1040. Is that what you did? You might have made a mistake in telling TurboTax which state your income was from, or in entering the state information from your W-2.
I don't know what you mean about filling out your W-2. Do you mean the W-4 that you give to your employer? Your New York employer should be withholding New York tax from your pay, not New Jersey tax. If your job in New York is your only income, or almost all of your income, you should pay little or no tax to New Jersey.
It sounds like your 2022 tax returns were correct. If so, compare your 2023 New Jersey and New York tax returns to the 2022 tax returns and see what's different.
