No, according to our proposed design they each have their own 'generic seller' uuid, and they share a Product.  To start a transaction, a JWT is produced with the public_id of the product, webpay receives the JWT, queries that product in Solitude using its public_id, retrieves the individual generic seller uuids for each of the supported payment providers, decides which payment provider it wants to use, then starts a transaction with that specific seller uuid for the selected payment provider.