Buyer: a supplemental tax bill comes a few months after closing. It's not in this split. See T12, and total cash to close in T03.
Seller: put this credit or charge into your net sheet in T21. Ask the HOA for the demand so dues are paid through the right date.
Many people get this wrong: “the seller already paid the December tax, so the buyer owes nothing.” That payment covers July through December. The buyer pays the seller back for every day after closing.