If someone is at rest in an inertial frame, his acceleration is $0$. He can use $F=ma$. The total force on him is $0$.
An occupant of the non-inertial frame of a rotating space station wants to do the same. If he is at rest in his frame, his acceleration is $0$. He would like to use $F=ma$, but there is a problem.
Without anything exerting a force on him, he would follow what an inertial observer would see as an unaccelerated path. The occupant sees that path as accelerated.
To fix this, he explains the cause of the acceleration as a pseudo force that acts on everything. By using this force, he too can use $F=ma$.
If the occupant stands on the floor, he is at rest in the accelerated space station frame. The floor exerts an upward reaction force on him that opposes the pseudo force. The total force is $0$. $F=ma$ works again.
For more on this, see Coriolis Force: Direction Perpendicular to Rotation Axis Visualization
Update: Some extended comments are likely going to be moved to chat. Adding content here.
When thinking about problems like this, it is important to keep two different frames of reference straight. Often you work in an inertial frame because $F=ma$ there. Sometimes you work in an accelerated frame because you can choose one where motion is simpler. You need to think about these frames separately.
In an inertial frame, the occupant of the space station is traveling in a circle at uniform velocity. This can only happen if the total force on him is just right to deflect him from a straight line to a circle. This force is call a centripetal force. In this case, the force is the reaction force from the floor of the space station. This reaction force is the centripetal force.
In the frame that moves with the space station, motion is simpler. The occupant and the space station are at rest. In this frame, there is no centripetal force because the occupant is not moving in a circle. He is at rest.
In this frame, motion is simpler, but the laws of physics are more complex. His motion is accelerated without anything exerting a force on him. He explains these acceleration as being caused by pseudo forces. Everything in his frame has a centrifugal force acting on it. Everything moving also has a Coriolis force. With these forces, he can use $F=ma$.
So the forces acting on the occupant in the accelerated space station frame are the centrifugal force and the reaction force of the floor. Centrifugal force pulls outward on him. The reaction force keeps him from falling through the floor. These forces are equal and opposite. The total force is $0$, exactly as expected for an occupant at rest.
Note that motion is significantly simpler in the accelerated frame.
If the occupant wants to keep track of the position of a point on the ceiling, it is easy in the accelerated frame. Both are at rest. The distance and direction to the point stay fixed. He can set up x, y, and z axes with himself at the origin and easily calculate the distances and angles.
In the inertial frame, he is moving in a circle. The ceiling is moving in a circle with a different radius. He can set up the same x, y, and z axes. The calculation is simple at the instant where he passes through the origin, but both positions are functions of time. In this frame it isn't so immediately obvious that the distance and angles to the ceiling stay fixed.