Your eyes are probably better than mine. I thoughts that the slots were mostly covered, meaning the outside ring is on, compressing. The pullers are for that. It there are two pieces in the picture, then the pullers work. If not, then correct, you don't gain by pulling and pushing on the same part. I tried screw drivers and about crushed the nose ring. I could not get the motor out with the collet in place.
I never put the collet on quite so far again. It will potentially stick if it bottoms out on the shaft.