Zoysia is a warm season grass that grows best when temperatures are between 80 and 100. Zoysia seeds should NOT be planted in the fall when cool season grasses are normally planted.
Start planting your cool season grass seeds when the fall temperatures reach 75° and are dropping as fall / winter approaches. Fall is the best / least risk planting time for cool season grasses. Alternately the second choice is to plant in spring when spring temperatures have reached 60° and are rising in the spring -- again this is not the BEST time to plant cool season grass.
So the answer is no, you should not spread the seed at the same time.