The redirect was not working because I didn't use redis as store.type. With 'phpsession' as store.type in config.php of SimpleSAMLPHP, my session was lost immediately after successful authentication. After installation of the predis client I managed to login into Moodle via the IDP (SimpleSAMLPHP with LDAP configured as provider).
We are having similar issues with the logout piece. We don't have Redis installed but we do use memcache. I'm not a developer so I'm not sure if I can simply configure the saml2 store to use memcache instead?