You can add Producer credits to your releases at any time by visiting your Credits page, even if your release is already live in stores!
To do so, just head to the album page of the release you wish to edit. Click on "Credits"
From the credits page, click the "Add New..." dropdown menu and select "Producer."
After you have selected the Producer credit type, you can choose a specific type of producer in the following drop down. For simplicities sake, I chose just "Producer". After you have selected these fields, you can go ahead and enter your Producer's name. You can also optionally add their email (producer emails will not be shown on streaming services).