Skill modifiers apply to main skill or keep separate?

In this example damage is added to the main hit, not only to additional fragments.
Vile Eruption is more useful (mathematically) for spam DEE than Cooldown I think

For Cooldown you probably go for Path of The three from Oathkeeper and level Occultist to just 32
and use these points for some other Poison source optimally. Or maybe 1p if you level Occultist higher for some reason.

Some info here Secondary Skill Modifiers