Under what context do kills add towards bounty progression in Destiny?

I have been playing Taken King on Xbox One, and so far, bounties have been pretty self explanatory.

Today I picked up a bounty for killing a certain amount of enemies, in a certain amount of time, for a total of five times using heavy weapons. I then proceeded to patrol The Moon, and complete patrol missions.

In a battle, I killed an enemy with the heavy, before swapping to my primary. Apart from that one enemy, I did not even inflict damage with the heavy. After the battle, I found I had earned 1/5 towards my heavy bounty.

Later on, I scored a multi-kill with my super ability. This counted towards the bounty, aswell.

I was then notified, while not engaged in combat, that I had earned another 2/5 of my bounty. The bounty soon completed, with me barley bringing out my heavy, to begin with.

I thought that maybe it had counted kills from nearby players? I was not playing in a party, or as part of a fire team. Perhaps it is a bug or a glitch, but this makes me question the actual inclusion towards bounties.

What counts towards a "kill X amount of enemies in Y seconds, Z times, with a certain weapon type" bounty?