How do you log in to DirectAdmin when you create the very first database for the user? If you log in to DirectAdmin directly with the username and password, it should work in phpMyAdmin. However if you log in to DirectAdmin as the "admin" user and then click "Login as USER" when you create the first database, then you will not be able to log into phpMyAdmin using the user name and password for that DirectAdmin user account. Because of this, it is important that the first database that is created in a user account, always is created by logging directly into DirectAdmin with the own user name and password for that account. It only happens when you create the first database in a account.
Edit: So what you could try to fix a account like that, is to change the DirectAdmin password and in Enhanced skin it should have a box to check if you also want to change the default database password. Likely that will fix it for existing account.