Hi Apurva,
There are several constants in the SAML module that control this behavior. Sounds like you need to adjust the DefaultLogoutPage constant to target your desired page when logging out. For example, you can set it to /SSO/ which will start the login process automatically or you can use index.html. I included the part from the SAML documentation below that explains this as well as a link to the documentation.
DefaultLoginPage – You can specify a different login page here for when the login process fails. When the end-user cannot be authenticated in the external IdP, a button will appear, and by clicking this button, they will be redirected to the specified login page. If this is left blank, an unauthenticated user will be redirected to /login.html.
DefaultLogoutPage – Removing the sign-out button is recommended, but if you choose to keep it, the end-user will be redirected to a page. You can choose where the end-user is redirected to (for example, back to /SSO/ or your login.html page). Every user signed in via SAML is redirected to this location when they are logged out.
SSOLandingPage – Set this if you redirect the index.html to log into your app automatically. See Using SSOLandingPage for further information about this.