Are you talking about 2021 or 2022? What is "it" that is still calculating New York tax?
If I understand you correctly, you should have two W-2s. One W-2, from the New York job, has only New York information in boxes 15, 16, and 17. The other W-2, from the New Jersey job, has only New Jersey information in boxes 15, 16, and 17.
When you do your New York tax return, TurboTax will ask you how much of the income from each W-2 was either earned in New York, or earned in another state (i.e. New Jersey) while you were a New York resident. Page 2 of the New York part-year resident tax return, Form IT-203, has two columns for income. The left column is "Federal amount" and the right column is "New York State amount." The federal column will have your total income from both states. The New York column will have the amount of income that you earned for working in New York, plus the amount, if any, that you earned for working in New Jersey while you were still a New York resident. The way the tax is calculated is complicated and confusing, but you pay New York tax on only the income in the New York column.
