There’s a growing number of websites that allow subscription to site notifications that alert you when new content is posted. These will notify you like any other Windows 10 app or service. But, there’s a couple Windows 10 settings that can inadvertantly keep this from working correctly.
In Windows 10 Settings go to System – Focus Assist.
Make sure to configure the Automatic Rules settings appropriately. For example, if you have a multi-monitor setup the “duplicating my display” needs to be turned off. Additionally, consider if the “app in full screen” option may be hindering the feature from working for you.