Imagine you are on a theme park ride in which you sit in a car and are spun around in a circle, basically like a giant centrifuge.
An observer from the outside would say that there is no centrifugal force acting on the person in the car, only centripetal. However, for the person in the car, there is the force pulling them inwards (centripetal), and its reaction force pushing outwards against the side of the car (centrifugal). However, from this point of observation, the person in the car is stationary and everything else is moving around him.
Does this not mean that there is no circular motion in this frame of reference, and therefore the reaction force is not centrifugal, as there is no circle centre? Basically, I am confused as to why a fictitious centrifugal force will show up in a frame of reference where circular motion is not occurring.