The SCLogin module is simply a front-end to Joomla's login component (com_user). When a user enters their username and password and submits the form, we had those credentials off to the com_user component which then checks if the credentials are correct or not. If correct, com_user will look and see if a redirection URL was passed and push the user to the correct page after they login.
However, if the credentials are wrong, the user will be redirected to the Joomla login page. There's no way to override that behavior unless you want to modify Joomla's core files, which we wouldn't recommend. Additionally many components will automatically redirect the user to the login page by default if they try to access restricted content for registered users only. For that case alone, we'd recommend doing what you can to improve the login page through template overrides or styling to make it fit with the flow of your site since users will inevitably get there.
The SCLogin module is meant as a convenient replacement for the standard Joomla Login Module (mod_login). It's not meant to replace the entire Joomla login or registration process for 'normal' users. JFBConnect integrates smoothly with the SCLogin module and has an option to automatically add the social login buttons to the Joomla login and registration age as well.
I hope that helps,
Alex