Autotag your browser on the apps timeline as Browsing. If you don't have 'When first AT is matched skip the rest' checked, you should now have some time double tagged.

Open Autotag editor.
Check When first AT is matched skip the rest (at the bottom).
If Browsing autotag is not at the bottom of the list, then move it there.

So now it will first match any sites you have, the rest will be filled up with Browsing autotag.

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If you will add a site to a new (non existing) autotag, you will have to open AT editor and give it higher priority (move it up), because newly created autotags are appended to the end.