In this answer here, I give a mathematical explanation why the surface of a rotation fluid is a parabola (or paraboloid, if you consider 3 dimensions). After you spin the fluid and the "parabola is formed" you drop the ball. If you don' have an external force to keep the ball on a given trajectory, after some time it will be located at the center. For a better understanding, look at the subject of stable equilibrium and the harmonic potential ($V\propto x^2$).
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