This is a recurring closing cost. All recurring closing costs will be prorated by escrow.

So if the closing date is the 13th day of the month then the seller will pay the 13 day proration and the buyer will pay for 17 days (assuming an HOA payment for example).

Same logic holds for property tax except the transition dates will align to the property tax biannual dates. Of course the property tax payment for the buyer is always an estimate based on the previous assessment. The county will send out the adjusted payment a few weeks/months after escrow closes.