It means, the more recently it has paid out, the less likely it is to pay out again. Or, the longer it's been since a win, the more likely it is to give one. In other words, it isn't truely random, it "compensates" for big wins or losses, to maintain its percentage payout over time (usually measured over 100000 games).
I'd say independant, simply because I can't see different companies cooperating that much. The temptation to be the one to give the big win, and therefore screw over every other game on the box and make your game the favourite, would be too great.