It works on the principle that a sub misbehaves in order to get attention. To a sub, attention usually means 'play' and to many subs the common BDSM punishments (whippings and so on) are not punishment at all but fun things that they enjoy. So, by punishing bad behavior with something they enjoy you are more or less ensuring that this bad behaviour will continue.

So, by removing attention, you are discouraging the behaviour you want to correct instead of reinforcing it. Just as with children in a classroom - the kid who plays up often does it for attention so instead of giving that attention you send them out of the room to cool off (usually 5 minutes is enough). They are not getting attention so they stop playing up.

I would not say that it needs to be complete silent treatment. Not at all. More that it needs to be complete 'no play'. You can talk to them about other things - have they done the dishes, how was their day and so on - but you do not interact with them in a BDSM context. You cancel any plans you may have had to play, you don't threaten them with any BDSM style punishments. You effectively withdraw from the lifestyle for a short time.

You can also impose punishments that are tedious and boring as opposed to the exciting and interesting ones. For example, sitting or kneeling in the corner facing the wall, writing lines, cleaning something really hard to clean (the old army cliche of using a toothbrush to clean the toilet...)

All of these ensure that there is still contact between sub and Dom but it is not exciting and interesting for the sub - in other words it is an effective deterrent without risking the relationship.