Logout redirect for front-end users in WordPress, in this case Authors with access to the back end to add posts. Redirects to a front end page called 'Members Home'.

wordpress-logout-redirect.php

//AUTHOR LOGOUT
	add_filter( 'logout_url', 'author_logout_page', 10, 2 );
	function author_logout_page( $logout_url, $redirect ) {
		$user = wp_get_current_user();
		if ( in_array( 'author', (array) $user->roles ) ) {
			return home_url( '/members-home/' );
		}
	}