The institution of any appeal under sections 270C.924 and 270C.925 from the order of the commissioner does not stay any proceedings for the assessment or collection of taxes against the property involved therein. Notwithstanding such appeal, the commissioner shall file with the auditor of the county in which such property is situated an order confirming, increasing, decreasing, or determining the net tax capacity thereof, and the county auditor shall extend and levy against such property, or the owner thereof, the taxes thereupon for such year according to such assessment, and all subsequent proceedings for the determination of the taxes and the collection thereof shall be taken as if no appeal from such order were pending. When the matter is finally determined on review a properly authenticated copy of the findings, order, or judgment shall be filed with the auditor of the county in which the land or property referred to in the proceedings is situated. If such order or judgment lowers the net tax capacity of the land or property referred to in the proceedings, the commissioner, upon petition of the owner, approved by the county board, shall abate so much of the taxes against such property as is attributable to the excessive net tax capacity thereof. If such tax has been paid, the county auditor, upon petition of the owner, approved by the county board and the commissioner, shall refund so much of such payment as is attributable to such excess net tax capacity. Upon such refund being made the county auditor shall charge the same to the state and the various governmental subdivisions thereof that participated in such excessive payment, in proportion to their respective shares therein, and deduct the same in the next tax apportionment.