When I make an inclined cilinder and apply copy rotation with an empty, it rotates as if the z axis is also inclined. However, when I try the same method with this Venus model I found online, the object keeps rotating on a vertical z axis. Any way to fix this or is the problem with the model I found?
See its local orientation, it is not aligned with her body (maybe you have rotated the object then applied its rotation, which has aligned the origin with the global orientation, but it has lost the original orientation):
To realign the origin correctly, select some faces of the base and create a custom orientation:
Enable the Affect Only Origins option:
Align the origin with the custom orientation:
Switch back to the Local orientation:
Rotate the origin 180° on X:
Disable the Affect Only Origins option, now it should work: