According to a tutorial that shows how to export my NLA to Unity I need to apply all modifiers first. Though, I noticed that if I apply my armature to the mesh then the mesh stops following the armature. I also have a mask modifier on the mesh that maybe makes some fuss. But it doesn't seem to matter if I apply both modifiers in any other order. The mesh still does not follow the armature. I've appended the blend file in comments if someone could take a look.