Here is my take on it.
When you close the throttle the pressure in the inlet pipework from the turbo (compressor) to the throttle plate is dead ended. This can damage the turbo but it causes the compressor to slow down or stall and will take time to come back up to speed. This causes a lot of lag during gear changes.
A diverter valve recirculates the boost back into the inlet to the turbo and a dump valve vents to atmosphere, pssss. This takes the load off the compressor and allows it to maintain a higher RPM so taking less time to spool back up to speed.
The problem with some dump valves that vent to atmosphere is the type of fuel system. If you have a system that has a air flow meter before the turbo, the dump valve vents to atmosphere "metered air" and causes the engine to run rich as the ecu is injecting in the amount of fuel for the air that has passed the meter not what has gone into the engine. If you have a map sensor, this measures the inlet manifold pressure so it is not bothered by a atmosphere dump valves as he has not "seen" the air yet
Hope this makes some sense, (been a long day

)
Steve.