Time remapping always works on the start and end time of the resource, not the layer. If you have a trimmed clip in a composition and you want to time remap just the trimmed part of the clip, do this:
- Pre-compose the trimmed clip moving all attributes to the new comp and trimming the new comp to the length of the layer.
- Apply Time Remapping to the nested comp (the Pre-comp in your main comp)
The first Time Remapping keyframe will be at the first frame of the layer; the second keyframe will be after the last keyframe of the layer. That's all there is to it.