In every case where the Auditor provides for redemption under this article he shall, where such redemption is made prior to January 1, 1947, direct the assessor to enter and back-tax such property, as other property should be entered and back-taxed for the assessment year 1945 and each and every year thereafter in which the same has not properly appeared upon the land books of such county. In those cases where redemption is made after January 1, 1947, he shall extend and collect taxes at proper valuations and rates for all assessment years after the year 1945. No compromise shall be made under the authority of this article for direct property taxes for the year 1945 or thereafter: Provided, however, That nothing herein contained shall prevent the Auditor from redetermining value and taxes for the year 1945 and thereafter in the manner otherwise provided for by law in case of redemption of property which may have been sold to the state for nonpayment of taxes, or be delinquent, or forfeit for nonentry.