When selling your property, you are required, at settlement, to pay the rates up to and including the settlement date. In practice, the Vendor will pay the rates to the end of the current rating period and the Purchaser's share of the rates will be apportioned in the settlement statement and paid to the Vendor by the Purchaser.
If the second instalment is from 1 October 2017 - 31 December 2017 and settlement is on 10 November 2017, the Vendor will commonly pay the rates up until 31 December 2017 prior to or on settlement.
As the Purchaser will have possession of the property from the settlement date onwards, they are required to reimburse the Vendor for the rates from 11 November 2017 - 31 December 2017. This will be reflected in the Vendor's settlement statement which is given to the Purchaser prior to settlement.