If you received a payment from CSI or CMRRA, this payment represents both writer and publisher portions of the settlement, as would a regular payment of mechanical royalties (by CMRRA). As such, it is incumbent upon the music publishers who are recipients of a market share payment to distribute, in accordance with the provision of their relevant publishing agreements, a portion of the payment to the writers associated with the publishing catalogue(s) for which such payment was received. This also applies to any other rightsholder(s) associated with the publishing catalogue(s) in question.
If you received a payment from SODRAC, this payment covers the writer and/or publisher portions originally collected by SODRAC. These rights are generally paid directly to each rightsholder. Music publishers who received a payment from SODRAC on behalf of one or more writers, or on behalf of any other rightsholders, are responsible for the distribution of the applicable shares to those parties based on the contractual agreements entered into with those parties for the musical works in question.