Hi, even in private windows, Firefox shows the latest downloads. My guess is that you don't mind Firefox having that list as long as you choose when to see it.
As a first step to regaining control, you can stop the automatic display of the download list for each download:
(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button accepting the risk.
More info on about:config: Configuration Editor for Firefox. Please keep in mind that changes made through this back door aren't fully supported and aren't guaranteed to continue working in the future.
(2) In the search box in the page, type or paste browser.download.alwaysOpenPanel and pause while the list is filtered
(3) Double-click the preference to switch the value from true to false
