League of Legends (LoL) Question: Is Gangplank not enhanced R on-hit and/or DoT (not counding cannonball wave

I know that since it's not on the tooltip it means it doesn't, but for some reasons I have the impression that GP's ult has a kind of on-hit (like proc-ing Grasp.) That or I don't get how some targets who managed to escape R's zone die right afterwards (less than a second, but still outside R area.) If not counting the expected cannonball waves (I get that they're intrinsically damage over time,) does it have any other (post-)hidden DoT not described? - Same about his Q, does it do any delayed DoT without any related item or rune? As even when watching pro matches, it seems that after the main damage, there's a delayed second (or multi/DoT) one which finishes off the target who escaped with a tiny amount of health. (I'm aware that Grasp and other runes are procced by Q)