The Auth Connector has to be installed (or reinstalled) to enable the SAML options for Auth Connector-as-IDP, and have the IDP certificates generated. And SAML has to be set up.
The promptless capability is provided by Windows Kerberos/NTLM SSO transactions.
Firefox browsers, however, do NOT support Kerberos/NTLM SSO transactions by default. However, you can configure this ability by a Firefox config setting.
How to Enable NTLM SSO in Firefox: