If you look at the one scene in the movie where Corbin is shown smoking:
You’ll see that he smokes the cigarette in a “normal” direction. That is, what looks to be white paper filled with tobacco on the end to be lit and brown paper that we associate with the filter in his mouth. You have to pay attention to his cigarette dispenser to get the joke:
You’ll notice that it says “quit smoking” and “to quit is my goal” on it. Prop reproductions show that the branding for the device is “4 the day” and that on top is a refill cartridge.
So, this seems to be a device marketed and designed to help people quit smoking by weaning them off of cigarettes. The device only dispenses four cigarettes a day (meaning you’d have to space them out to about one every four hours to get your “fix” throughout the day) and the tobacco to filter ratio is such that you could only get a couple of puffs (and they would be very weak).
Corbin even says “what a day to quit smoking” (or something similar) during the climax when he only has one match left for the “fire” stone.