Issac Newton described an experiment in which a bucket containing water is spun. As the water in the bucket starts to rotate, it becomes concave. The reason for this can be understood in terms of rotating frames of reference.
Newton supposed (as an axiom of mechanics) that there are frames of reference (a system of locating particles in space relative to an origin, and in time) in which his 3 laws of motion are true, and momentum is conserved. Such a frame is called "inertial". If one inertial frame exists then any frame with an origin that moves at constant velocity relative to the inertial frame is also inertial.
As I mentioned, the existence of inertial frames is an axiom of Mechanics. The truth of the axiom is verified by observation. It can't be proved. If a frame of reference is rotation with respect to an inertial frame, then the rotating frame is not inertial, and Newton's laws (in their simplest form don't hold). Instead of "F=ma" there are extra terms for the Coriolis and centrifugal force.
In the case of a spinning space station, it is spinning relative to an inertial frame, and that is why there is a centrifugal force.
For Newton, the bucket experiment proves that there is a notion of "absolute space". This interpretation is not accepted by all, and in particular, Ernst Mach rejected the idea of any absolute space. His ideas were influential on Einstein.
You can read more about Newton's bucket experiment at http://www-history.mcs.st-andrews.ac.uk/HistTopics/Newton_bucket.html and you can read about Ernst Mach's ideas regarding absolute space at https://en.wikipedia.org/wiki/Mach%27s_principle