Virulent Quills are a bit confusing and some people do not understand what they do exactly. I recently got them and decided to do some testing to see exactly how they work.
-Each quill has a chance to explode and cause poison to all surrounding enemies (though this chance is so small I dont think it matters). The chance to explode from the initial firing only appears after 4 quills have hit a single target (so the 5th quill and on). [note: I have only seen this twice so it might be a bug which causes them to go off]
-Once a quill is on a enemy then broken it has a much higher chance to explode. The explosion looks and acts like a Fiery Vaporizer with knockback (the mist only lasts for 0.5-0.75 seconds). There is also damage from the explosion hurting everything in the blast.
-Shock ticks break quills and also cause the explosion so pairing the quills with Electron Vortex will provide the best poison coverage for a group.
-The poison caused by the blast seems to be High poison (it lasted as long as my DVS poison).
This has just been my very limited testing, if anyone has found my info to be wrong please tell me right away.
I wish I could try to help you, but I don't really know much about Virulent Quills. All I know is that a quill has a chance to cause a poisonous explosion.