Normally, if the website directed the download link to a new tab (as a popup), Firefox will close it right after showing the Download dialog (Open vs. Save).

However, if you directed the download link to a new tab, for example by middle-clicking the link, Firefox leaves it open. Is that the scenario? I don't know if there is a solution for that.

When I click on the download link on most sites 'Internet Download Manager' is opened and downloads the file and do not see that Download dialog box where I choose the folder to save the file and no extra tabs are opened. But some sites cause a blank tab to open while 'Internet Download Manager' downloads the file.

Oh, I don't know how IDM works. Maybe they have a workaround for this?