Box 16 of your W-2 is correct. NY can tax all your income, including your earnings after moving to Illinois. That's because, when you work partially within and partially without New York State during a tax year, NY considers the out-of-state portion to be taxable by NY unless you are required by your employer to work remotely and are assigned to a bona fide office of your employer in the remote location, and are not working remotely for your own convenience. This is known as the "convenience of the employer" rule, which a few states employ. This NY Tax publication gives the details of that policy:
https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
Since your your NY Box 16 includes all your income, your employer regards your remote work as subject to NY taxation.
IL can tax only the income you earned after you became an IL resident.
Since you moved during the tax year, you should file as a part-year resident in each of the two states, and allocate your income accordingly. You will allocate 100% of the income from your NY job to the NY return; you will allocate only the portion earned after you became an IL resident to the IL return.
IL will give you a credit for the NY tax you paid on the portion of your income taxed by both states. That portion - not the full NY Box 16 amount - is the "Illinois base income taxed by NY." You may have to calculate the pro-rated NY income - and the pro-rated withheld NY taxes - manually.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
