Are you getting any error in the logs while login with native users and able to login into hub console with native users?
SSO is basically to allow external users to login when they are authenticated. Also most of the SSO implementation will skip the IDD login page.
Should you want the Native Users also to login with SSO, may be you need to extensively change the SSO code and the login provider to have both the types of users login. Might not be a easy or an advisable option.
Depends on your SSO config but below works for us for native users.
Can you share application logs with error message.
Do have you made any changes to login provider too ??