Lands owned by the state and acquired pursuant to the provisions of title 21 of this article, exclusive of the improvements erected thereon by the regulating districts, shall be assessed and taxed in the same manner as state lands subject to taxation pursuant to title 2 of article 5 of the Real Property Tax Law, provided, however, that the aggregate assessed valuations of such lands in any town shall not be reduced below the aggregate assessed valuations thereof with the improvements thereon at the time of their acquisition by the regulating districts, and provided further that in case of a general increase in assessments in any town the assessed valuations of the lands and improvements at the time of their acquisition by the regulating districts shall be deemed to have been increased proportionately with the increase of other real property in such tax district. The taxes levied thereon shall be paid by the river regulating district under whose authority the land was acquired.