I agree with you that you should not be held accountable for their portion but often the supplemental property tax bill is not calculated by the tax assessor for 3-6 months past the close of escrow . We have forms that we provide to the Buyer and also in the escrow instructions it states that the buyer needs to be aware there may be a supplemental tax bill for the time that the buyer owns the property from close of escrow . But I have never had this situation so expert help is needed. If they don't know they will be able to direct you to someone who can.
Barbara Robbins-Olexa, Broker, e-Pro(R), SRES(R)
L B Brokerage