How to use many TimeLines as Prefabs in Unity?

This is to complicated to explain in text so I provide a video (sorry, a South Park Episode is played in the background )
Basically I want to create 3 types of prefabs where the player can walk up stairs, climb a box, or climb a ladder. But when I create a Timeline the current player position is "saved" inside the timeline and teleports back if I move the Box (similar to when you create an Animation outside a Gameobject... If you move it it, it will teleport back to where the animation was made)....

Any idea how to solve this or what I should google to find out more?
Thanks!