No, not at the time. Each box belongs to each download box.
If you had them separate by enough text to never see them into the browser's window at the same time, you might want each of them to show its own popup.
I can't think a simple solution right now, since the shortcode consturctor doesn't know the existence of the other shortcode for me to determine whether it's been already added or not, and finding a way to do it would hurt others who do want the popup in each box.
By the way, I wonder whether the links are working at all for your example.
Between the opening and closing square brackets sets [db]here[/db] should go a working link, not a single text with a file name… and drag/dropping an icon from the desktop would make a link to that computer's file, depending on your computer's OS, not to a remotely hosted file, if the browser ever does anything with a drag/dropped file into wp editor.
My plugin only changes the EXISTING link attributes (source, alt text, css style for the icon) but it does nothing whether it doesn't find any link attribute to change.