If it's the rotational spinning of the station that cause the ball to drop towards the floor and allow the person to stand in one spot with out floating about; AKA artificial gravity. Then both are moving in a circular motion in the same direction. Why wouldn't the ball according to the laws of physic which state an object in motion will continue to stay in motion until acted upon by another force or something to that affect; Stay in motion until hitting the floor, and because the floor is also in motion, cause the ball to bounce back to whence it came prior to it being dropped.Earth has actual gravity caused by the mass of its composition. This is not the same thing at all. We're not dealing with gravity on a space station, only inertia. It would just 'feel' like gravity to us on board.
Stick with the interior of a more modest space station - easier to explain. Our frame of reference is external to the station and not rotating, so we see the station rotating. Peer inside and...
Whilst the person has a grip on the ball, both have inertia, but a centripetal force is acting on both the person and the ball from the floor of the station, pushing upwards towards the centre of rotation. The ball shares this force (let's keep things simple and assume the person is rigid throughout). If nothing happens both the ball and person describe a circle within the confines of the station due to its rotation and return to their starting positions after one rotation of the station. Crucially, both have a circular motion.
When the ball is 'dropped' no further force is acting on it, so it will continue in a straight line from our reference point. However, the person continues in a circular motion because the station floor is providing a centripetal force.
But the person is not in the same frame of reference as us, their frame of reference is rotating. So, from the persons perspective the straight line movement of the ball in our frame of reference appears to be a curve. They will perceive the ball falling in an arc until it hits the floor, at which point it will eventually stop moving due to friction.
Would look like this. https://space.nss.org/dropping-the-ball-in-a-rotating-space-settlement/
Cheers,
Drew.
Perhaps I'm missing something but if one throws a ball upwards from their seat aboard an aircraft, regardless of how fast the craft is going the ball will come down again to the same location.that it was prior to it being tossed upward. It works the other way also, if one tosses a ball at the floor on an aircraft, it will bounce back to it's origin.