When exactly do you have to pay for Finder's rule Responsibilities to the Dead when you move something?

When exactly do you have to pay for Finder's rule Responsibilities to the Dead when you move something?

There are two cases where Finder of Paths Unseen must pay:
  • When it moves a piece in a way that decreases the Health of a damaged Dahan or Invader so it has now taken lethal Damage (one of many ways Finder's action can destroy the Dahan/Invaders with its own action);
  • When it moves an Invader/Dahan in a way that directly triggers their destruction by another action (Finder directly triggering their destruction by moving them).
The first case can happen by causing a Health penalty (e.g., Pushing a damaged Town/City into a Sacred Site of Rising Heat of Stone and Sand) or removing a Health bonus (e.g., Pushing damaged Dahan out of a land with Infinite Vitality or Gathering a Blight into a land with a damaged Durable Town against Habsburg Monarchy Livestock Colony Level 4).
The second case most commonly occurs in conjunction with Powers like Melt Earth Into Quicksand and Call to Guard and when teaming up with Ocean's Hungry Grasp to Push Invaders into the Ocean (but not when moving Heart of the Wildfire's Presence, since moving the Invaders/Dahan isn't what triggers Blazing Presence).
If something prevents the destruction, then Finder does not need to pay. If one triggered action triggers another triggered action that causes destruction (like moving pieces into another Spirit's Bargain of Coursing Paths, which then moves those pieces into another Spirit's Melt Earth Into Quicksand), this does not count as "directly triggering" the destruction.