Attack: time starts ticking down after the creature dies.
Damage Reduction: time starts ticking down after you take damage. I tested it and let a weak creature attack me for 5 minutes, and the time only started to tick down after I removed my equipment and took the first hit. In addition, gaining XP will also make the time tick down.
Bonus XP: Yes, time will start ticking down after you gain XP.
Improved Loot: Yes, time will tick down, even if the creature doesn't drop loot, as shown in the image below: