WPS animation time

I read several places that weapon damage counts as ONE SOURCE of damage over time. But maybe I misunderstood this. I’ve been rethinking it… So weapon damage added to abilities which does not deal damage WITH a weapon, still stacks independently with a weapon attack skill? So in the case of shadow strike, you deal that damage with your weapon. So dots from say, attacking with WPS like execute - or another skill that uses weapons like RF, do not apply each their dot (only the strongest).

The confusion for me stemmed from reading many comments that weapon damage attack dots don’t stack. So to be sure I got it right this time - since dreeg’s evil eye is an ability that does not deal damage with a weapon, the %wpn damage added to the skill still applies a seperate dot?

Sorry if my thoughts appear clumsy, I’m not a native English speaker.