One of the reasons for an ESCROW is that they collect the Property Taxes from the Seller, up to the date of Close of Escrow: If the Seller is paid up, (usually), then they will receive a reimbursement check.
And they will collect a pre-pay check from you for the pre-pay taxes: Taxes are always pre-paid, in six month intervals:
The first installment is for July thru December and is due November 1st
The second covers January thru June and is due February 1st
The amount of taxes that the Escrow company will collect, is determined by the month that the Escrow closes; eg. 6 month's worth in January, or 1 month's worth in June.
Unless there are additional levy's, the normal tax rate is 1.25%.
Good luck and welcome to California