Player A has a Defiant Greatmaw and a Grizzly Bears. There is no counter on either.
Player B plays Splendid Agony putting one counter on each of player A's creature.

Will Defiant Greatmaws ability trigger? I.e. who is actually placing the counter on the greatmaw?

I am quite confident that it will not, but would like some rules reference. Especially since you in game play usually place your own counters/dice on your own creatures.

Hi,

Thanks for your question. No, the Greatmaw will not trigger. The Greatmaw's ability triggers if you (the controller of the Greatmaw) puts a -1/-1 counter on the Greatmaw. It will not trigger if the opponent is putting the -1/-1 counter on the Greatmaw. Player B is placing the counters from the Agony, since they control the spell that's distributing the counters. It doesn't matter who is putting the counters for tracking on the Greatmaw, the only thing that matters is who controls the spell or ability that's putting the counters on it, and in this case, that's Player B, not Player A.

Thanks,
Nathan Long
Magic Rules NetRep