I really don’t know how that can happen.
Are the media and zip file you can see in the location Dropbox/Apps/your dropbox folder/Data/ ?
Do you have a copy of your dropbox folders also on your local machine? I use that as well. You need to install the DRopbox app: https://www.dropbox.com/en/help/4454
How large is the .ged file? The backup process is not quick. Perhaps it is not finished
Last idea: check your server logs for errors at that time related to the backup to dropbox module..