Probably the most common procedure taught by the technical diving agencies is that whenever you have a failure that causes you to start losing gas, you first shut down the isolator. The theory behind this is that you know you will at least have saved half your remaining gas. We do not advocate this approach.
If you go to the isolator first, you get no confirmation of what the problem is, which means you have to go to one of the posts anyway. So in every case you'll need to shut down at least 2 valves. If you go to the post first, in the most likely scenario (1st stage failure) you'll only have one valve to shut down. You solve the problem faster, get started on your exit faster, reduce the amount of bubbles blowing around your head faster (which may be bringing clouds of silt down on your head if you're in a wreck/cave).
Effectively we're using the odds of failure. The types of failures that would force you to need to isolate would be:
Burst disc failure
Tank neck o-ring
Manifold o-ring
The chance of a burst disc failure, tank neck o-ring failure or manifold o-ring failure are extremely small during a dive. The pressure in the tank is continually decreasing and ambient pressure is increased as compared to the start of the dive.
On the other hand, regulator 1st and 2nd stages have a number of o-rings and moving parts, which are constantly being used throughout the dive. Therefore by far the most likely failure will be a regulator failure (1st or 2nd stage) which can be solved by shutting down the post.
So if you can speed resolution in the most-likely case, why not do that?
In addition, you can usually identify the location of the failure. If the HP seat in the 1st stage fails, then the 2nd stage will begin freeflowing. So if your necklace reg begins freeflowing, you know you have a left post failure. Likewise, if your primary reg starts blowing gas uncontrollably, your right post has failed. If the failure is such that it is not delivering high pressures to the 2nd stage, and is instead just blowing gas straight out of the 1st stage, you can usually identify by sound which side this is coming from. Note that this even works with thick wetsuit hoods. Again, if you hear the gas blowing from the left side, it is likely a left post failure; gas blowing from the right side is likely a right post failure.
So the procedure we use is as follows:
Try to determine where the failure is.
If you can identify the side, shut that post down.
If you can't identify the side, then shut your right post down - this is the most likely failure (since it is the regulator being used most actively)
Breath the reg down (or hit purge button) to depressurize line
If bubbles stop, you solved the problem. Get your buddy to look at it to see if it's fixable. Fixable or not, you should probably exit
If bubbles don't stop, isolate. Get your buddy to take a look and see if they can identify the problem.
One final note - whenever you contact (or come close to contacting) the "ceiling" (roof of cave, roof of wreck, etc.) you should always do a run-through of all your valves. Reach back and check that each of the valves is turnable and on.