I actually discovered this principle by accident, when I wanted to try something else with ring magnets.
Thoughtlessly, I assumed that the magnetic field within the ring would have the same direction as the field on axis level outside of the ring.
But my experiment did not work out.
So, I drew the conclusion that the field characteristics are more like on the drawing on the left.
Meaning, the magnetic field on axis level inside the ring works in the exact opposite direction.
So, it is understandable, why the cylindric magnet shoots into the ring all of a sudden, although the influencing forces are very complicated.