Yeah, alum, usually potassium alum, is just a solid block of one of the ingredients used in antiperspirants to plugs up sweat glands to keep you from sweating as much. That’s partially how it works as a styptic - it’s irritating, so blood vessels will contract, but it also just plugs up some of the smallest vessels. Its use was much more common before the widespread adoption of electric razors, even if just as a little styptic pencil.

Yes, I’m one of those hobby shaving people.