In a written statement, the certificated flight instructor (CFI) reported that the purpose of the flight was to provide the student pilot training. The student pilot made several approaches and a practice hover autorotation before repositioning the helicopter to a different area of the airport. They planned to perform more hover autorotations and the CFI continued to guard the flight controls. The CFI deviated from the normal procedure they had practiced of communicating and counting down before rolling the throttle to the closed position. The CFI initiated the hover auto without communication. In response to the movement the student depressed the left [improper] anti-torque pedal and the helicopter began to spin. The CFI could not regain control and the helicopter rolled. The CFI further stated that the accident could have been prevented if he had briefed the student more thoroughly on the maneuver and if he had assumed authority of the controls earlier in the maneuver. The CFI reported no pre impact mechanical malfunctions or failures with the helicopter