@Francois
Yes, if your URL rewriting is not working correctly then you will have to use the http.php extension. This is indicative of URL Rewriting not working correctly on your server, at least for this specific URL.
The way it should work is that you call api/tasks/cron and api/.htaccess should rewrite the URL to api/http.php/tasks/cron for you. Take a look at api/.htaccess for yourself.
Cheers.