Not sure if I understood the requirement correctly but based on your example if you want user id 151 before 150 then you should have two sorting columns. Something like:
$result = $this->link->query("SELECT * FROM tickets WHERE ID IN (SELECT MAX(ID) FROM tickets WHERE Type=0 GROUP BY User_ID) ORDER BY USER_ID DESC, ID DESC");
Also check that you don't sort the data somewhere in the code after getting it from the database.