They don't claim the credit for it... They enjoy Reggae music and they are trying to spread the sound. No different than a hip-hop or a techno DJ. They aren't just talking over the song yelling Kya Bamba. These artists create dubplates, and include the sound systems name for example :Kya Bamba, Barbass Sound, Love Alliance Sound, and Jaffa Sound.
All the artists creating (singing) the dubplate produce it with the Sound System, and are paid for creating such mix.
Hopefully, that helped a little.