Well, I can say that having run dogs who then stumbled upon wild cougars, the dogs know the cougars are there loooong before the cougars get a chance to pounce on anybody. And the dogs are generally pretty fearless about the giant kitty, and kitty ends up a tree rather quickly. It's when the cougar has been watching the dogs in their own yards and sets up an ambush that dogs get eaten.
Cougars are methodical hunters. They like to watch their quarry and follow it for a while before deciding whether it's worth the risk to tackle it. They know they can win most fights, but have to weigh how likely they are to be injured. If they don't like the chances they'll pass it up for easier prey. And once you're aware of one, it ruins the hunt. They HATE when you make eye contact and try to slink away real fast.
I bet those tiger masks people wear in India would work well on cougars.