Re: It's unclear how the handover of control from the student to the instructor was performed
Small helicopters have a double yoke. Each person in cockpit can easily reach and share the cyclic stick.
They also have doubled pedals, just as a dual control car does, so taking control of the tail rotor is a non-issue, basically informing the student "my aircraft".
The collective pitch control typically resembles an old-fashioned handbrake lever and sits between the seats.
So no real issue at all unless the student screams "NO! *MY* aircraft" and initiates a pissing match.