In the lab frame there is no centrifugal force. The ring goes outside because it lacks of a centripetal force.
Let's take a step back: if the rod spins slowly then the ring does not slide out because of the friction. In this case the friction is a centripetal force, this means that it is responsible for keeping the ring on a circular motion. If you increase the spinning velocity, then the friction force hits its maximum, after this it won't be any more enough to keep the motion of the ring on a circular trajectory; so it will simply spiral out.
Let's move to the ring frame of reference so imagine to be sat on the rod and do not look anything but the ring. As the rod is spinning slowly the ring is fixed (we don't see any movement with respect to the rod). Still the friction is acting (as before), but now is not to keep the ring on a circular motion, but is to counteract a mysterious centrifugal force which comes only because you are in a rotating frame of reference. As the rod spins faster and faster (and so our frame of reference) this centrifugal force gets bigger and bigger. When it overcomes the friction the ring start to slide out.
Maybe it's easier to visualise if instead of rotating the rod, you just accelerate it in the longitudinal direction. Increasing this acceleration, at certain point the ring will start sliding with respect to the rod, but the cause is in the rod, not in the ring! If you look this from outside the ring would just like to stay in its position while the rod slides out.