The seller concessions are simply treated as a reduction in the purchase price. You are allowed to claim a tax deduction for property taxes assignable to the dates you owned the property, as if you paid them directly to the assessor, even if someone else paid them. Likewise, the seller is only allowed to deduct the portion of taxes assignable to the dates they owned the property, even if they paid the entire year and did not get a credit back from the buyer. (It's part of the law that only the owner can deduct the property taxes, so when the owner changes, the deduction is split on a pro-rated basis.)
You do need to be aware of when taxes are calculated and paid in your area. For example, in New York State, county taxes are calculated from January 1 and payable by Feb 15, while school taxes are calculated from July 1 and payable in September (I think). Which means that if you buy a home in June, you could claim a deduction for about 7/12ths of the county taxes, plus 1/12 of the school taxes from the previous year, plus the entire school tax bill that was paid the September after you bought the home.
