try this
$sql="SELECT u.id AS userid
FROM user u
WHERE u.username IN('".implode(',',$results)."')";
you missed single quotes.
dont give aliase name in where clause
dont use {} in mysql
EDIT:
change this
$userids = $DB->get_records_sql($sql);
echo $userids;
to
$userids = $DB->get_recordset_sql($sql);
foreach ($userids as $ids) {
$userid = $ids->userid;
echo $userid;
}