You set what you want to appear in the parameters of the module. I assume you know you can set "Media" as one of those items. Controlling how the media is presented is also set in the module parameters (direct link, inline mp3 player, All Videos Reloaded).
Whether the download icon appears is set in the individual media file record itself. You can see the module at work at my church's site:
www.calvarychapelnewberg.org/.
The downloads show as I've selected "media" as one of the items to show.
Check to make sure "show download icon" in the media record.
tom