The Manager reports download as soon as they are finished running. No email just a download popup. I’m not sure what will happen if the manager logs out of Docebo while the report is running. 

yes agree...the download should still be available but that may depend on your browser and system settings...I use a Mac and Chrome and the downloads go directly to my downloads folder so logging out after the download is no issue however if they close the browser or logout during the export, the download cannot complete and there is no file to download.