Based on a topic about shotgun weapon dps I was running some parses on the dummies in agartha to determine whether the Double Barrel Shotgun added damage was added to the attack, or included. My results were interesting in that it demonstrated the extra proc was not always occurring. Below are copy/paste of my combat log.
First lets start with a normal shot.
You start using Raging Shot.
(Critical) Your Raging Shot hits (Normal) Anima-Sim: Dungeon for 2537 physical damage. (museum proc)
You successfully used Raging Shot.
Your Raging Shot hits (Normal) Anima-Sim: Dungeon for 599 physical damage. (double barrel proc)
Your Raging Shot hits (Normal) Anima-Sim: Dungeon for 6817 physical damage. (regular hit)
Next you can see a crit, followed by a normal shot
You start using Raging Shot.
You successfully used Raging Shot.
(Critical) Your Raging Shot hits (Normal) Anima-Sim: Dungeon for 17271 physical damage. (no extra damage)
You start using Raging Shot.
You successfully used Raging Shot.
Your Raging Shot hits (Normal) Anima-Sim: Dungeon for 560 physical damage. (extra damage)
Your Raging Shot hits (Normal) Anima-Sim: Dungeon for 6975 physical damage. (non crit)
Bug occurs with a regular raging shot
You start using Raging Shot.
You successfully used Raging Shot.
Your Raging Shot hits (Normal) Anima-Sim: Dungeon for 6698 physical damage.
You start using Raging Shot.
From my tests it seems the bug is most often occurring on critical hits, but also impacts regular attacks.