Bug Spine rotation causes strange offset

Hello everyone. I've run into a strange problem recently. I have a humanoid character with a simple animator with reloading animation. The character also has a script, that rotates the spine in root bone space in LateUpdate. Also, I have a debug sphere parented to the head bone, and before applying spine rotation I set the sphere to transform to some point in character space (p.s. by root and character space I mean the same thing - the root space of the character).

So the expected behavior is this: debug sphere is not affected by the animation, and it's rotated by procedural spine modification.

This works only if the spine rotation angle is 0, otherwise, the sphere sways a lot. I also tested it by rotating the spine bone in local space, but they had the same issue.

Does anyone have an idea why it happens? I suspect it's the way Unity updates transform, but I'm not sure. Also, how can I achieve the desired behavior described above? I really appreciate any help.

Video of the problem:

Code (CSharp):

1. public class SpineRotation : MonoBehaviour
2. {
3.     [Range(-90, 90)] public float angle = 0;
4.     public Transform sphere;
5.     public Transform spine;
6.     public Vector3 offsetMS;
7.    
8.     private Quaternion Rotate(Transform space, Transform bone, Quaternion rotation)
9.     {
10.         return space.rotation * (rotation * Quaternion.Inverse(space.rotation) * bone.rotation);
11.     }
12.    
13.     private void LateUpdate()
14.     {
15.         sphere.position = transform.TransformPoint(offsetMS);
16.         sphere.rotation = transform.rotation;
17.         spine.rotation = Rotate(transform, spine, Quaternion.Euler(angle, 0f, 0f));
18.     }
19. }