Facebook determines where the action should appear. If you go into the Activity Log area inside Facebook (by clicking the "Activity Log" button in the bottom right of your cover photo), you should see the action of joining a group in there. To the right is a circle, which when clicked shows different options like "Let Facebook choose whether to display on my Timeline" or "Always display on my Timeline".
The default is the first option for Facebook to choose, and that can't be changed. Depending on the amount of users that have taken that action, the viewer looking at the Timeline, and lots of other social factors, Facebook will determine if that specific action should be shown. The same goes for the Recent Activity module, the 'Ticker', and other social channels.
Basically, it's better to have more actions posted to user's Activity Logs. From there, Facebook automatically determines how to show that to the user's friends. The more actions posted to more Activity Logs, the 'higher' the importance and social relevance that action becomes and the more likely it is to show up in more prominent channels.
Finally, Facebook is constantly changing how things appear and what their factors are. They used to post everything, but that became way too spammy. So, now, less is posted, but when it is, its generally looked at by users to be more relevant.
Hope that explains, but if you have any questions, please let us know,
Alex