Can anyone assist me on this below:

I have a database called appdb. I need to grant access to this db to different users say: api_user, app_user, portal_user. 

So I created a ROLE as APP_ROLE and GRANT as below:

GRANT SELECT, INSERT, UPDATE, DELETE ON APPDB.* TO APP_ROLE;

Later I assign the Role to user:

GRANT APP_ROLE TO API_USER@'%' IDENTIFIED BY 'YOU';

SET DEFAULT ROLE APP_ROLE TO API_USER@'%';

But the problem now is:

Application team want to choose the database when they establish connection. But they couldn't use APPDB. 

So they couldn't see  any db objects listed in APPDB. Is there a way we can assign a default database also for user.