The very short synopsis of the theory is, you need co2 to access the oxygen in your blood. Too little can cause a sense of panic and air starvation like when you hold your breathe but too much can also. There is not enough for that effect in normal air, it has to come from your "waste" co2.
Most people breathe too much on average dumping too much c02 and basically living in a mild panic attack all day every day.
In other words, fast breathing can cause a panic attack the same way a panic attack can cause fast breathing.
It is worth noting that over breathing can increase inflamation, especially in the nose. It is your bodies way of trying to trap some of that escaping co2.
The breathing exercises from those methods help you reset your breathing to nasal only and slower, awake from that panic threshold. It takes time though.