In Jefferson County whenever an error is found in the calculation of the amount of ad valorem taxes due or any mechanical error is found in the tax return, listing and valuing of property by the tax assessor upon assessments legally made, the tax assessor is hereby authorized to correct the same in his or her records. The tax assessor shall file in the record the proper evidence to support his or her action, and shall immediately certify same to the tax collector, and if a refund of taxes is due, the tax collector shall refund the monies out of the next monies collected. The taxpayer shall furnish proof of such payment to the satisfaction of the tax collector within two years from the date of such payment.