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?

When a Dahan or Invader is pushed in a way that:
  • Decreases the Health of that 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);
  • Directly causes something else to destroy that Dahan or Invader (Finder directly triggering their destruction by moving them).
The first case can happen by causing a Health penalty (e.g., Pushing into a Sacred Site of Rising Heat of Stone and Sand) or removing a Health bonus (e.g., Pushing Dahan out of a land with Infinite Vitality or Gathering a Durable Town into a land with Blight against Habsburg Monarchy Livestock Colony Level 4).
The second case most commonly occurs when teaming up with Ocean's Hungry Grasp to Push Invaders into the Ocean, but can also occur with Powers like Melt Earth Into Quicksand and Call to Guard.
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 to their destruction), this does not count as "directly triggering" the destruction.