In inertial frame.
There is no centrifugal force. The reason the string is under tension is because it pulls on the object in order to keep it centripetally accelerating to travel in a circular path. The reason the object flies away when the string breaks is because it continues to travel in the straight path.
In a rotating frame. (Frame rotation matches rotation of the object.)
Object is stationary. It's not moving at all. So the only explanation for the tension in the string is gravity-like force pulling on the object, forcing it away from center. That's the centrifugal force. When the string snaps, that force accelerates the object away from center.
The centrifugal force is a fictitious force because it does not exist in an inertial frame of reference. It only manifests when we try to use Newton's Laws to describe motion in an accelerated frame of reference.