When you attack a target with Arrow Spray and use after that Poison Arrow on the target, only the initial hit gets increased for 45%, but not the dot dmg.
Edit:
German translation doesn't mention only direct dmg portion
When you deal damage with Arrow Spray, you cause enemies hit to take 45% more damage from the direct damage portion of your next Snipe, Scatter Shot, or Poison Arrow used within 5 seconds.
You see that direct damage bit there? The item explicitly states only that the initial damage of poison arrow is affected, it doesn't say anything about the DoT getting buffed, which is why you are noticing that the DoT does not get buffed.
Yeah @kengur22 it is only for the direct damage. Many 1 and 2 set weapons work that way. The Maelstrom daggers for example, along with status effects like Empower.
I just wish it increased the direct damage of acid spray. I always love exponential curves.
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I'm wrong with this bug i blame the German translation for this set. It says it increases the dmg of the next Snipe, Scatter Shot or Poison Arrow, there isn't mentioned that it should only increase direct dmg.