Remember to list the FBX export options:
- Select Armature + Meshes
- Export FBX
In Include panel
- (tick) Selected Objects
- (select) Mesh and Armature
In Transform panel
- default
In Geometry panel
- (untick) Apply modifiers
In Armature panel
- (untick) Add leaf Bones
In Animation
- (untick) Key All Bones (this might be the one causing for unwanted animations)
Remove the step asking to unpack textures as files