(a) The sheriff shall account for the proceeds of all redemptions included in such list in the same way he or she accounts for other taxes collected by him or her.
(b) All real estate included in the first delinquent list sent to the Auditor, and not accounted for in the list of redemptions and certifications, shall be deemed to have been redeemed before certification, and the taxes, interest, and charges due thereon shall be accounted for by the sheriff as if they had been received by him or her before the sale.