I don't think such an addon exists or that ESOlogs could tell you.
For the later: If players choose to be anonymous you cannot see who did what, so this would be 1 reason it cannot say for sure (only if your group got the setting disabled it would be able to I guess, but not automatically. You'd have to search where a fight starts and who did what before).
And I also doubt an addon for this case would be a good idea: It needs to be able to tell you that properly in all cases as you'd need to track all effects/buffs whatever could get you into combat before you get into combat. And it would also track that after combat started maybe, until it ends. But that way it might miss the next start as this can happen really fast after another. This would be a very performance hungry addon which would need to run all the time and monitor a lot of data + track it (means write to SavedVariables! Else you could not check it later on and data would be lost after a loading screen).
Try to use voice/text and educate the guys, speaking is easier. If this does not work, well, they would not even care if you'd tell them you got it written who was the one
Probably they'd only feel caught and blamed, and be even more <whatever> (if this was your intention).