What is damage you do vs. damage a creature takes? (and Dark One’s Blessing)

The Warlock ability Dark One’s Blessing says (emphasis mine)

Starting at 1st level, when you reduce a hostile creature to 0 hit points, you gain temporary hit points equal to your Charisma modifier + your warlock level (minimum of 1).

Is there a general ruling on who or what is the author of damage? Most spells and attacks are written to describe how the target takes damage, rather than how the attacker does damage. I think it is safe to assume that an attack you make or a spell you cast is you doing damage, but I am unsure on how to rule in a more abstract example, such as forcing an interaction with a damaging environment.

Consider the following hypotheticals. None of them are my specific question, but serve to illustrate what I am trying to come to terms with. My question is whether there is a general underlying principle in the game that assigns authorship to damage.

For example, suppose oil has been spread on the floor and a hostile creature chooses to cross it. My warlock throws a lit torch into the oil and the DM requires an attack roll. The subsequent fire reduces the creature to 0hp. Does the warlock get to use Dark One’s Blessing?

Suppose the same warlock lights a nearby patch of oil on the floor and the DM does not require an attack roll. A hostile creature later chooses to enter the burning oil and is reduced to 0hp. Does the warlock get to use the ability? Did he reduce the creature to 0hp, or did the fire? Does it matter that the creature chose to enter the fire through its own movement – if the warlock had been able to use a spell or action to force the movement, would the answer be different?

Finally, consider three warlocks who all have initiative before a target. One throws a flask of oil on the floor, one throws a torch that ignites the oil, and one uses a shove attack to move a hostile creature into the space where the flaming oil is / will be. Which warlock(s) get to use Dark One’s Blessing? Does their order matter? That is, is it a different answer if the shove moves the creature to the space where the oil will be, vs. to a space where the flame already is?

Possibly related: If my familiar is forced through my action to drop a rock while over a target, is it considered an attack?