You are correct:
Just connect the relay between the 12V supply and the Open Collector output.
The reason for the Open Collector output is two fold: i) higher current capable. ii) The supply voltage does not have to come from the same supply, as long as it is not greater than the webbrick supply and the two supplies have there common connected (labelled 0V or G typically). So if you want to switch something that takes only 9V that can also be done common the 0V of the two supplies, connect the device to 9V and the other end to the open collector.
Technical comment:
The reason the supply cannot be higher than the webbrick supply is because the circuit is protected from back Emf by a diode that clamps the PIN to the webbrick powqer rail.