Ok So I did the test and now I know everything about this mechanic. Not sure what you did wrong Demhar (maybe you had midshot set not working properly?). I was testing this without gearswap. My results are quite straight and disappointing.
Ok lets start
First Relic+3 body and cape.
2207 is capped damage
You can clearly see that when double attack proc, 2nd hit is doing 2891. 2891/2207 = 1.3099 so almost exactly expected +31%
Now disappointing part:
When triple shot from body proc, it really becomes a triple shot (more on this in Oshohi mask part of test) and all Double Shot damage gear is useless...
Oshohi mask:
It seems to be exactly the same as other Double attack damage gear. It works the same and its % increase
I changed body to Tatenashi to avoid Triple Shot proc first and equipped NQ Oshohi Mask.
Like you can see my new capped regular hit is 2148 after those changes (it went down a little because I was using Malignance head before Oshohi, so pdl was adding a little)
With NQ Oshohi and cape I had total of "Double Attack" damage +40 And nothing surprising here. 3007/2148 = 1.3999, so again 2nd hit doing almost exactly expected 40% more.
Finally Cape + Body + Mask for +51% total and chance to Triple Shot:
Same result again
First hit 2148 and 2nd hit 3243. 3243/2148 = 1.5097, so again almost exactly expected +51%. You can also notice the same for crits, 5999/3973 = 1.5099
Lastly something that confirms Triple Shot proc really make Double Shot and true Triple Shot:
All +51% damage Double Shot doesnt work when Triple Shot proc, but "Triple Shot" Damage +10 from Oshohi mask activated on 2nd and 3rd hit. 2362/2148 = 1.099, which is again almost exactly expected +10%.