HI Pondus,
Thanks for sticking with this one.
I attach a screen shot which I hope will help. I am no longer sure that this is related to Safari. I assumed that it was because it came up in a Safari session (many times) and it made reference to accessing a website. However, It might just be an Avast issue and the screen notifications might not be within Safari, just on the screen. That is certainly what this screenshot would seem to show, as the Safari window is not open but the Avast notifications are still present.
/Users/AlanSally/Desktop/Screen Shot 2018-01-12 at 15.56.14.png
/Users/AlanSally/Desktop/Screen Shot 2018-01-12 at 15.55.51.png
What do you think?