The starting point is that all income, from whatever source derived, is taxable unless there is an exclusion or exemption in the Internal Revenue Code or elsewhere. 

The city seems to think that it's income; that's why they issued a 1099. 

The increase in property taxes over the next ten years may be deductible, subject to SALT limitations until they expire and are not renewed. 

I wouldn't say that the payments from the city reduce the basis of the property.  "Generally, a taxpayer is not required to reduce the purchase price or cost of property acquired with a governmental energy-efficiency incentive that is not a rebate. Many states label their energy-efficiency incentives as rebates, but these incentives may not in fact constitute rebates or purchase-price adjustments for federal income tax purposes."

https://www.irs.gov/irb/2013-47_IRB#NOT-2013-70