CMX log for evidence:

Note that I cast Endless Hail, then Bound Armaments, then Bound Armaments again, then I swap.
The first tick of damage occurs while I'm still on my bow bar (as seen in the log), and yet I do not get the Thunderous Volley bonus damage.
Quick note: the fluctuating damage is due to stats changing on swap (Nirn mainhand on DW bar) and the Berserker enchant proccing/expiring later.
Further note: the delayed application of Volley damage is silly to begin with, but the current state of the skill/weapon now requires a
4-skill backbar rotation in order to actually benefit from the bonus damage, which is very dumb.