There's no way for me to know the reason why notifications aren't available in a browser, so I don't think I can be more specific on the message. But we'll add troubleshooting info to the docs.
To receive a push notification for these, you need to go to the Hashtags page and click the 'Edit' link for the hashtag (not the Edit Tag button), like you're going to mute it. Then you can check the 'Web/App Notify' checkbox. In that regard, as in others, they are just regular emails sent to the group. This is different from the moderator notifications, which are sent to individuals only. My expectation is that most people won't use the `Web/App Notify` functionality; I think of it as a nice to have. I think the push notifications are more important for moderator notifications.
At some point, I will proactively create these hashtags for groups, if they don't already exist.