In order to get the Last Updated Module to show there must be some updated Downloads.
Note that when updating to show it is a real update you also need to set the "Has it been 'Updated'?" option in the Publishing tab to Yes as well as setting the Modified Date.
Also see the jD Oprions setting "How long is a Download UPDATED"> in Pictures and Buttons tab. This sets a duration in days that a Download is consider to be in a modified state