That's pretty much how it works, like an ignition coil in a car; 12 volts in and a gazilion volts out. I got one about two years ago and got a lot of use out of it for my outdoor bar. Sadly, I dropped it and broke the handle part where the battery is held.
They do well for small insects, but don't work especially well with wasps for some reason. Let me tell you, they are NOT happy after getting a taste of about 2KV. I've also found that moths tend to catch on fire and they stink!
"But the guy at Home Depot said it would work."