progressive slot machines, how do they actually work?

So I’ve always stuck to roulette and the occasional video poker, but lately I’ve been eyeing those giant progressive slot jackpots flashing on the floor. I sorta get that a little piece of each bet goes into the main prize pool, but I don’t totally get how it works behind the scenes. Is it just random when the jackpot drops or does it have to hit by a certain amount? Also, do you actually have better odds playing max bet or is that just something people say? I know discipline matters more for some games, but these slots seem like a different beast. Curious if anyone’s tracked this long-term.