In my case the activity post actually shows while I have activity auto-refresh activated, but this option also means that once I scroll down through the group activity feed under the most recent posts at the top of the feed appears a button saying “load latest” which when clicked shows all the latest blog posts (from the standard WP blog), which I do not want to have shown in all my groups.
So, I have deactivated the auto refresh to get rid of this, but have to refresh to see what I post.
I would like to find a way to adjust settings of which of my blog posts show in which groups (by tags or categories), but without the weird behaviour, but I guess that is another topic.