To be more specific, this part of the deal is called the Excelsior Jobs program. It rebates to Amazon 6.85% [0] of the wages earned by the company's employees, which effectively does mean that income taxes get paid out to Amazon (in reality, the income taxes paid plus a little more due to the NYS tax brackets [1]).

That being said, there's no city-level income tax rebate. Assuming the tax brackets currently in effect hold steady until the full 25k jobs promise was fulfilled, the city of New York would get ~3.8% of $150k * 25k jobs = ~$142.5 million/year once the 25k job mark is reached [2].

[0]: https://esd.ny.gov/excelsior-jobs-program

[1]: Note how the 6.85% bracket only applies to income above $215.4k; income above $1.08 million gets taxed at 8.82%; consequently Amazon will get more rebated than employees paid in income tax the vast majority of the time. See the second table of page 57: https://www.tax.ny.gov/pdf/current_forms/it/it201i.pdf#page=...

[2]: The ~3.8% is approximated based off of page 69 of https://www.tax.ny.gov/pdf/current_forms/it/it201i.pdf#page=...