As you say Louis, the liferafts do their own thing with the HR automation once they go underwater. The line you mention was referred to as the Painter line in my P&O days?
Foreshore, The HRM consists of a double looped white rope line, a release mechanism and a Red Weak Link breaking strength.
The strong white rope is secured to the deck or liferaft cradle and attached to the liferaft lashing with a sliphook. If the ship sinks, the water pressure will (within 4 metres) activate the sharp knife which cuts the white rope and the liferaft will float free. As the ship sinks, the liferaft painter line will be stretched and the liferaft starts to inflate. The Red Weak Link breaks and survivors can board the floating liferaft.