Suggestion Box

The notification being described can be seen in your middle screenshot. Directly to the right of the Address bar (where the URL is for the website) you will see the name of the page you are on with (1) next to it. So in this it's (1) Writers of Substance Gr... where that number is indicating the number of new notifications you have from the site. That will show up on the tab whenever you have a new notification no matter if you're on that tab or any other.