I've read the discussions about this item stacking faster with Runaan's because of the 2 extra shots it provides. So will the splash damage from Tiamat and Ravenous Hydra also cause this to stack faster? How exactly does the stacking from attacking work?

It would not stack faster with Tiamat because the splash doesn't apply on-hit effects. The Hurricane does apply on-hit, which is why it speeds up the Shiv's charges.
The proc on Shiv doesn't happen as often as Ionic Spark did but the timing can be better in the right conditions. If you just stand in one place and auto attack, Ionic Spark is better. If you are juking in a poke fight then the Shiv is better. The Shiv is also always up when you move from one location to another, like changing lanes, chasing, falling back or jungling.

oic. That makes sense.

so think of this on draven, crit for his passive, and he moves a lot to catch axes, and attacks a lot to maintain said axes, he will be getting LOTS of procs on his own, also champs like MF whos q not only lets for double hitting but hitting an extra target will get lots of stacks as well, however how will it work on say, ezreal's q, and worse yet, forget hurricane, everyone be very very afraid of teemo with hurricane..........