@sxweb Thanks for the additional info. Are you sure that _spineAnimator is the same SkeletonAnimation GameObject that [SpineAnimation] public string _onDeadAnimation; populates its list with? By that I mean that it might be that the list is from another SkeletonAnimation component, listing other animations, and then setting this animation at _spineAnimator leads to a mismatch.
If _spineAnimator for sure contains this named animation, could you please send us a minimal Unity project that still shows this issue? You can send as a zip file to contact@esotericsoftware.com, briefly mentioning this forum thread URL so that we know the context.