In cyber-physical systems, the digital shadow of the physical system may gradually degenerate and deviate from reality, causing cyber-physical inconsistency. This is a major problem since consistency must be constantly preserved for accurate remote control of the physical system, raising a need for immediate identification and correction. In this paper, we investigate cyber-physical inconsistency for immersive telerobotics. We give a state-of-the-art survey, investigating different forms of cyber-physical inconsistencies and showing how they can be handled. We propose a software system for immersive telerobotics, which unifies the approaches for handling different forms of cyber-physical inconsistencies, such as real-time virtual reality immersion into the robot environment, feedback for operator hands through exoskeleton gloves, timestamp labeling for motion tracking, and, synchronization of operator arm to robot arm coupling through vibration feedback; within a single framework. We have successfully applied our software system to an immersive telerobotics scenario, showing that it is a step forward towards a holistic system enabling both availability and consistency in telerobotics.