It seems that if Anyone on the team removing burn or poison reduces the cool down if koros moves.
This effects all present koros on either team.
Noticed effect in tower pve and recently in PvP. Sorry no screenshots but easy to replicate.
Just bring along a koros and someone to remove a debuff (yasmin nub zen or others)
If I'm reading skill right he should only get his cool down reduces if he does the purging of these debuffs.
Even easier to test it right now due to koros being in event dungeon. This effects him as well although he probably starts with all skills ready anyway.