Unfortunately, once an attack starts (and it can begin accidentally - a play chase that ends in a nip/scratch which causes a response from the other animal, escalating the situation, for example; often it is just over-excitement) prey drive can kick in and things get out of hand.
When instinct takes over, that's it - the animal will calm down afterwards, and may even be distressed and seem "contrite", but of course, the damage is done by then. It is always worse when there is more than one dog because the others will join in. I would add that this doesn't just apply to dogs - people are the same, as anyone who has read about crowd psychology will tell you. "The Pack/Crowd" takes over and individual will is subsumed.
We often forget that dogs - all dogs - are predatory animals. Many of them eg terriers and specifically bred to have lightening fast reactions, to react on instinct, and not to stop until their prey is dead. Others are specifically bred to guard resources and can become aggressive if those resources are threatened. WE have done this to them - we humans have bred these characteristics into them, and they can't be undone in a moment.
OP's dog is a wonderful housepet, and is normally (I would imagine) not a problem with most other animals, including cats - but when his territory is invaded, his guarding instinct kicks in; if the cat fell suddenly into the garden, or darted across it unexpectedly, his prey drive kicks in. It has never happened before, and will probably never happen again - and it seems that the cat wasn't really hurt, despite what the owners said.
The dog isn't a danger, despite that hysteria from one or two of the cat-owners on this thread.