It sounds to me like compile errors before any import takes place.
Can it be that you have extracted the Spine-Unity 3.8 runtime over the existing 3.7 runtime without deleting it beforehand? That would explain the errors. I will write a forum posting similar to Pharan's upgrade guide here to prevent some upgrade problems:
Spine-Unity 3.6 to 3.7 Upgrade Guide
Anyway, please re-download the unitypackage from the download page again, I have just fixed a different bug (related to import order that might cause error messages upon first package import):
Spine Unity Download
I have now created the respective 3.7 to 3.8 upgrade guide here:
Spine-Unity 3.7 to 3.8 Upgrade Guide