Erikari is right, but the right mesh in your image doesn't look like the triangles Spine should be generating. For example, I quickly clicked out a similar mesh and the triangulation doesn't look like what you are getting:
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In Edit Mesh mode, try unchecking Deformed so it is easier to see what is going on. It could be that your mesh is deformed and the triangles are good in the texture coordinates, but not in the deformed mesh.
