The rule is that you need que if what follows is a complete subordinate clause with its own subject and verb. Otherwise you omit que.
Je vais ranger ma chambre après avoir fait mes devoirs. -- I will tidy my room after having done my homework.
Je vais ranger ma chambre après que j'aurai fait mes devoirs. -- I will tidy my room after I will have made my homework.
In the first case you don't have a clause following après, just an infitif passé (avoir fait), hence no que. The second example sports a complete subordinate clause and therefore requires que.
-- Chris (not a native speaker).
