Are you saying the layering in Spine is correct, but the layering is wrong in Unity?
Are there multiple of this same skeleton in the scene? There's a known issue in Unity where it breaks draw order in favor of dynamic batching when there's multiple MeshRenderers using the same Materials. It's been there for a while but I don't know if they're ever going to fix it.
But in that situation, the solution is to add a "Sorting Group" component on the GameObject. That will force it not to batch and retain the correct draw order.
Losing batching here isn't a huge problem since multiple materials already break batching anyway.