When you put the collet on it will push down and tighten on the shaft as you tighten the prop nut. Prop adapters consist of the part you have in the pic, a collet that goes over that, and a prop nut.
Once the centerpiece is on and you tighten the but down or will squeeze that shaft VERY tightly. I would suggest you keep the prop off until you test motor direction on the plane. Inadvertently starting it up will hurt, make slashes, or remove fingernails.