Annual payments shall be ordered by an ordinance or ordinances of the legislative body. The ordinance shall further order a designated officer to notify in writing the county assessor of each county in which any portion of such property is located, of the city’s intention to make such payments. The county assessor shall thereupon enter upon the tax rolls of the county the amount to which any taxing district of the county is entitled under the provisions of RCW 35.21.430 to 35.21.450, inclusive; and upon delivery of the tax rolls to the county treasurer as provided by law, the amount of the tax as hereinbefore authorized and determined shall become due and payable by the city or town the same as real property taxes.