I found that the logs of Morph Browser and also of Sapot Browser show the websites I have been on. This way the Logviewer app will show my browser history even if I cleared it in Morph and Sapot respectively.
Apparently the Logviewer app retrieves the logs from journalctl. So there seems to be no way to prevent this persistent record (as opposed to 16.04 where the logs were deleted when the logged app was closed).
Do I miss something or is this a privacy issue?