I also faced the same issue and here is the way I solved it.
in class-wp-splash-page.php file add new function
public function get_cookie_name() {
return $this->cookie_name;
}
Then edit wp_splash_page_generate() in init.php as follows
function wp_splash_page_generate() {
wpsp_import_class( 'WP_Splash_Page', 'inc/class-wp-splash-page.php' );
$wpsp = new WP_Splash_Page();
$cookieName = $wpsp->get_cookie_name();
if ( $wpsp->is_active() ){
$wpsp->splash_page();
}
else{
unset( $_COOKIE[$cookieName] );
setcookie( $cookieName, '', time() - ( 15 * 60 ) );
}
}