When using the 250 MJ and 500 MJ manual dual stage regulator and the 160MJ dual-stage regulator kit, no, they can be either open or closed. As long as the cylinder in usage is open and both pigtails are connected. When the cylinder empties, the manual changeover valve is switched over and the corresponding gas cylinder should also be opened.
If you are using the 400MJ auto dual stage regulator, to operate it the auto changeover, both are open. To use it like a manual changeover, the reserve cylinder can be turned off (will have to be turned on when the first cylinder runs out). Both cylinders need to be connected to the regulator via pigtails at all times.