It sounds like you are using the wrong authentication type.
(on the same page)
Database Account Credentials utilizes database schema accounts. This authentication scheme requires that a database user (schema) exist in the local database. When using this method, the user name and password of the database account is used to authenticate the user.
Database Account Credentials is a good choice if having one database account for each named user of your application is feasible and account maintenance using database tools meets your needs
Yes, I know about that authentication type. Problem is our package is composed of many Apex applications. Using 'Database Accounts' auth type requires user to re-login whenever they switch from one Apex application to another.