Im going to try to explain it as best as i can.
Its like on beats and off beats - you can get on the off beats so you "double proc" auto is on the first auto of your passive 3 stacks granting you the first and second stack. You then auto again for the 3rd stack which gives you the passive bonus damage. Diana can be absolutely destructive with sated but it can also be lack luster on the time you get stuck on the off beats in the fight.
When stacking with the on beats your first auto gives you one stack and then the "double proc" auto with give you your second and third which with double activate the passive damage. 1 - 2/3, 1 - 2/3 etc.
It does this because the whole passive is linked to that third strike of the passive and with sated it essentially bundles it all together into the one hit.
Its super awkward now that I'm reading through it but hopefully you can make sense of it.
I know exactly what your talking about and have thought into it and i know that there is a pattern where your passive is still everything third though. I'm just trying to think about how to explain when it happens and its super hard ahaha