so i think they are trying to "simulate" a kolsch by cold condioning a beer fermented with ale yeast. i doubt they include kolsch yeast in the kit since there is only one dry kolsch yeast and it is discontinued.
what i would reccomend is to 2 weeks primary, 2 weeks bottle carb (preferably 3) at room temp then "lager " it cold around 8 or 9 degrees for as long as you can stand the longer the better up to about 3-4 months. then it might lose some flavor etc.
basically make the beer carb it up then cold condition it
so i just looked its k97. i never liked that for a kolsch yeast. it doenst taste kolschy to me.
k 97 temp range is 59 to 68 so they are asking you to keep cleaning up the beer at 59 degrees with that yeast for a while.
i would still stick with "lagering" it cold for a while to condition it. that will make a clean beer.