Blender Animation not working correctly

Hello,

I'm relativley new to Unity. I created a model in Blender with the human Meta-Rig and animated it. The animations look pretty fine in blender, but then I import the fbx file in Unity the head bone is not moving correctly in all my animations. The right eyelid is also not placed correctly. I already tried using a blend file and changing the export settings of my fbx. I also made sure to create keyframes assigned to the head's position and rotation in every animation. Unfortunately this didn't change anything.

Here's my recording of the problem: https://www.youtube.com/watch?v=6_eJhQi2nzw

Any ideas what could fix that?