Question about the Parshendi and the Desolations

For reference, I'm on page 798 of Oathbringer right as Kaladin Adolin Shallan and Elhokar are preparing to storm the castle with the wall guard and activate the Oathgate. Please do not spoil anything beyond this point

My understanding of the plot until recently was this. The Parshendi used to be voidbringers, but at the end of the last desolation they abandoned their gods for turning them into monsters. Gavilar wants to summon their gods which the Parshendi don't want so they have him killed. After being at war with the Alethi for ten years they get desperate enough to save their people and they embrace storm form start the everstorm and by extension a new desolation.

But with the recent truths revealed about the heralds this doesn't really add up. If the herald who was left behind giving in is what triggered the desolation then what, if anything, did the Parshendi have to do with it? Was the timing coincidence? Did I miss something or am I not supposed to know the answer to this yet?