Just based on what your inspector looks like, it seems like you're using a fairly old version of the runtime. Multi-object editing was added in October 2016.
There's also nothing special to do when setting sorting layers and sorting order.
Sorting is NOT a part of Spine's system.
The component inspector just exposes it because Unity's MeshRenderer inspector doesn't.
It's supposed to just work, as far as Unity's sorting system just works.
If your sorting layers setup in your project and your programmer's are different, I can imagine it doesn't work well. You would check Unity's help regarding that.