You are correct that your wife's unemployment - assuming it was not derived from employment in New York - should not have been taxed by New York. The "New York amount" on Line 14 of your 2019 Form IT-203 should have been zero. (But her unemployment should be included in the Line 14 "Federal Amount" column, since you filed jointly.)
https://www.tax.ny.gov/pdf/2019/inc/it203_2019_fill_in.pdf
See the instructions for Line 14 on page 24 of the 2019 instructions:
https://www.tax.ny.gov/pdf/2019/inc/it203i_2019.pdf
If this was not the case, then you will have to contact the New York State Dept of Taxation to dispute their findings. Their contact information should be in the assessment letter you received.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
