Alright, I know that regular pets do not have weapon damage, so they do not use the % weapon damage components of any devotions assigned to them.
What about pets that scale with player bonuses? Wind Devil, Storm Totem, Big Mortar, etc.
The answer is no, if anyone wants to know. As per Zantai, if the summon uses a weapon (like grimoire of nagosh skeleton) it will use the weapon damage part. In retrospect, obvious, but -_-
It also seems that summons that you can have multiple off have their own cooldowns for devotion procs. 3 Wind Devils surfing in a crowd fire off their own Falcon Swoops at their own pace (sometimes they came out almost at the same time).