No. These are two totally different concepts. The payment made to the performer(s) is the price charged for their performance, whereas the copyright belongs to the creator of the music, regardless of whether or not this is also the performer.
In other words, copyright fees must not be confused with the performer's rights, as both payments are independent, compatible and accumulable. If you are a member of the SGAE, we will pay you your copyright earnings, over and above any payment you may establish as an artiste for your musical performance..