Except they can't. It's continuous like regen, you lose 200 damage per second from fire trap and 100 damage per second from bleed, they stack for 300 health lost per second and I don't think the game can differentiate which is which.
Correct. All damage over time is applied together, and that application amy or may not kill the target as a whole, not individual effects. It knows how much damage of each type (fire, chaos, etc) you're taking per second, not where each part of those comes from, and the total damage is applied together, not in sequence.
In the case where something dies to a DoT, since which one is credited with the kill is arbitrary, the first one in the list* that could have killed it** is chosen and that's given the kill.
*The first one in the list will be the one that was applied earliest, and has thus been on the target the longest, except in the case of non-stacking replacing debuffs, such as blood rage, where replacing a debuff with one of the same type keeps it's place in the list - it's swapped out for the same one without anything else in the list moving up.
**This bit means that it ignores any DoT effects on the target that deal damage types to which the target is immune - if a CI character casts Blood Rage (chaos DoT) and then is ignited and dies to that, when checking through the list it will find the blood rage DoT first, but not give it the kill since the character is completely immune to chaos.
Kudos for explaining a complicated subject in a clear and concise manner.
