Imagine an observer in a space with a series of point like objects randomly scattered through it. Now suppose that the points are rotating around an axis that the observer is positioned on, let’s call the observer’s position O. Suppose the position of a given point is P. There will be a line from P to the axis of rotation that is perpendicular to the axis of rotation. Suppose the point that this line meets the axis of rotation at is called A. P moves in a circle with centre A and radius AP. There will be an angle between OA and OP, let’s call it x°; this angle determines how the motion of P is perceived by the observer. If x°= 0°, P would be on the axis of rotation and would not be seen to move by the observer at O. If x°= 180°, P would also be on the axis and wouldn’t appear to move but it would be in the opposite direction. If x° = 90°, P would be seen to move in a giant circle around O. Suppose for x between 0° and 90° P moves in an anti-clockwise circle, then for x between 90° and 180° P will move in a clockwise circle. Imagine you are floating in the middle of a spinning room, if the ceiling is spinning anticlockwise the floor will be spinning clockwise. The points that have x° close to either 0° or 180° will appear to the observer to rotate around a centre of rotation. There will be two different centres of rotation at 0° and 180°.
If the observer only saw points which had x° between 0° and 90° then they would see all the points rotating anti-clockwise and there would only be one visible centre of rotation. This could be the case if say the observer was standing on a disc which obscured the points with x° between 90° and 180° or if there were no points with x° in this range.
If the observer was standing on a large sphere then what they saw would depend on what part of the sphere they were standing on. If they were close to one of the two points on the surface which the axis of rotation passes through (the poles), they would see the points either rotate clockwise or anticlockwise depending on what side of the sphere they were on. They would only see one centre of rotation directly above the pole. If they were close to the plane that the points with x°=90 rotate around (the equator), they would see these points and rise and set. They would also just manage to see the two centres of rotations at 0° and 180°.
The model which most closely fits what we see on Earth is the sphere with the points as stars. The only difference being it’s the Earth that rotates. This is geometrically equivalent although physically distinguishable to the stars rotating. We see circumpolar stars in both the Northern and Southern hemisphere, in the North they rotate anti-clockwise and in the South they rotate clockwise. We see stars near the equator rise and set.
On a flat Earth all the stars would be at an angle of between 0° and 90°. Either because there are no stars below the Earth or there are but we can’t see them. On a flat disc Earth we would not expect to see two sets of circumpolar stars even when we are close the edge of the disc. If there were stars below the Earth, with x° between 90° and 180°, the only way we could see them was if we could visit the other side of the disc. Then we would see the other circumpolar stars. If there were only stars above a flat disc Earth then we would only ever see one centre of rotation. There is no reason at all why we would see stars rise and set near the equator on a flat Earth.