If the seller paid the taxes for the next six months when they were due why do you not expect to reimburse the seller for the portion of time you own the property? You need to ask the closing agent for a more detailed explanation of how the proration for property taxes works. Each owner pays taxes for the period of their ownership.
Taxes in most places in Michigan are paid in advance. So the July tax bill that was just paid actually covers the next 6 to 12 months. A purchase agreement typically calls the for the seller to pay the entire bill and the buyer to reimburse for their specific ownership period.
In Michigan, we pro-rate them back to the seller for the portion they've paid for the duration you'll live there.
So, just because they were paid last week has no impact on you or your closing -- they're going to pro-rate the summer and winter taxes back on a daily basis and then calculate how many days in each period you're going to live there. Based on that, they will add those fees to your amount due at closing and you'll be able to deduct those property taxes on your tax returns next year.
We run our taxes as such:
Winter: Dec 1 previous year - Nov 30 current year
Summer: July 1 current - June 30 next year
You have to PRE-PAY your Property Taxes;
whether it is through the Escrow or directly.
Pre-paid taxes are one of the items in your Closing Costs.
Depending upon the month you close, you will pay 1 to 6 month's taxes.
Haven't you gotten your HUD1 and had it explained to you?