You may be confusing the regulator and cutoff functions of the control box. They are actually separate mechanisms, and merely share the same box.
The cutout has one function, and that is to disconnect the generator AND regulator from the battery. As we mentioned above, WHen properly adjusted, the generator will put out at least 13.4 volts when it is turning with the engine. When you shut off the engine, the battery would back-feed the coils in the regulator and generator if there were no means to disconnect the battery...and that is where the cutout comes in. When the engine is turned off, the voltage in the system drops below the 13.4min volts it had when it was turning. So, the cutout needs to be adjusted to open it's contact at 13.3 volts max. It MUST open the contacts by 12.7 volts, otherwise the system will stabilize at the battery voltage of 12.6 volts, and the battery would slowly discharge by back feeding the generator. That is why the book says to adjust the cutout to open between 12.7 and 13.3 volts.
Now, to check the cutout, open the control box and visually look at the cutout contact. It should be open. If it isn't, then physically pull the contact open, as it may have welded closed. If you can then manually close the contact, or it closes back on it's own, and it stays closed...you need to adjust the screw to the point that it does open when you release it. This is all with the engine off.
Now, start the engine. The contact for the cutout may close immediately. If it doesn't, rev the engine to 1500rpm or so and it should close and STAY closed when you let the engine go back to idle. If it opens every time the engine idles, then adjust it to where it just stays closed so long as the engine is running and idling. Your idle must be at least about 750 or more. Below 750 it is common to have the cutout open anyway, until it is reved and the generator steps up the system voltage. If the contacts never close...then we need to check the generator voltage across the "D" and "E" terminals on the box, to make sure the generator is putting out at least 13.4 volts when reved.
So far all the conversation is concerning the cutout only. You can test the cutout actual voltage by testing across the "D" and "E" terminals on the control box.
If the cutout works, and generator voltage is above 13.4 to 14.4 volts at 2000rpm...everything is working as it should.
If the cutout never closes, and the generator voltage is below 13.4 volts at 2000rpm...then either the generator is not functioning or the voltage regulator is not adjusted/working. When the regulator section of the box is working, you should see the regulator contact (different from the cutout contact!) opening and closing at a regular interval while the engine is reved above 2000rpm. Once again, if the contact does not cycle, then either the generator is not working or the regulator is not controlling it.