Please bear this in mind when reading this: I've only been to this new dynamis system two times.
I'm unsure what has been said already on how to proc things. But i think i figured it out tonight and it's really simple. I've only tested the theory on MAGE mobs (Bard, White Mage, Black Mage). So this may not be true for everything, but i fail to see why it wouldn't be.
My idea was that each mob doesn't have a set proc. Instead, the mob just requires a certain action. For example in order to get the red proc on the Mage mobs it requires magic to be acted on the mob. So, i asked our mages to just spam dia over and over (This made sure that it wasn't the change of spell that caused the proc, it was just the action). By doing that we got the red proc on every mage mob we pulled untill we got kicked out. Some mages proced instantly, some mobs took 10 dias.
I didn't have time to look into it and test it further. But i assume the same applies to melee mobs. i.e Use WSs over and over and eventually it will proc red after X amount of WSs.
Sorry for being a 'troll' or whatever it's called. And sorry if someone has said this already. I'm unsure if they have, so i thought i'd just post what i found in the hope it will help someone :)