OK. Since you never actually worked in New York when you were a New Jersey resident, your work income during that time is taxable only by NJ.
However, since your wife worked partially within New York when she was an NJ resident, her income during that time is taxable by both states. This is due to New York's "convenience of the employer" rule, which states that a non-resident's remote income is taxable by New York if the employee works remotely for their own convenience, rather than that of their employer. NY's rule is explained in detail here:
https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
NY's "convenience of the employer" rule applies to NY non-residents or part-year residents whose assigned or primary work location is in New York, but who work both within and without New York during the tax year.
Bottom line: your income as an NJ resident is taxable only by NJ. Your income as an NY resident is taxable only by NY. But your wife's income as an NJ resident is taxable by both NJ and NY. Both your incomes after becoming NY residents are taxable only by NY.
You will be able to claim a credit on your NJ tax return for the taxes paid to NY on the income that is taxed by both states, so the same dollars won't be double-taxed.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
