i am not able to reproduce any issues. However with .m4a files, there is no cover type field in the file, so if you set it in MB then that setting only exists in the MB database. If you set it in another application then that application will have its own way of displaying a value but it wont exist in the artwork tag.
So when you convert the file in MB, unless you set the cover type in MB, then I would expect the type to say "Unknown". If you set the field in MB then it works fine