The centrifugal force tends to pull me "down" , but the floor responds with a "reaction" , keeping me at rest with regard to the cage.
A number of ways to test if two forces are not an action-reaction pair:
Do the two forces act on two different bodies? Here, the body in both cases is question is you: The upward force on you by the floor versus downward force on you be the fictitious centrifugal force. These are not an action / reaction pair.
Are the forces always equal but opposite? Suppose you try to jump. The normal force will increase, but the centrifugal force remains the same. These are not an action / reaction pair.
Does the action / reaction pair result from the same interaction? In this case, one of the forces is the normal force while the other is the fictitious centrifugal force. Once again, these are not an action / reaction pair.
There is a reaction to the floor pushing you up via the normal force, and that is you pushing the floor down via the normal force. You can see this in action (not recommended) by washing a load of jeans and T-shirts. After the water drains but before the spin cycle starts, rearrange the contents so the jeans are on one side and the T-shorts on the other. The unbalanced nature of the reaction can make the washing machine bounce around, perhaps even walk.
What about the reaction to the centrifugal force? There is none. The fictitious centrifugal force is the odd force out. It cannot be paired with some other force. More importantly, what centrifugal force? An inertial observer sees only one force acting on you, the normal force exerted by the floor. There is no centrifugal force. It's a fiction, designed so that we can conveniently use Newton's first two laws of motion in a domain where, strictly speaking, those laws does not apply.
Isn't the situation very similar to the situation at earth, where I'm attracted by gravitation instead of a pseudo force? Nobody would identify gravitation as a pseudo force, however, from the equivalence principle bot are the same and cannot be distinguished.
In general relativity, gravitation is indeed a pseudo force. In Newtonian mechanics, it is a real force. The Newtonian reaction to gravity pulling you down is you pulling the Earth up gravitationally.