OK, you give a scenario to create a group but you didn't replied to the question to know if the tables are shared.
Use the JMS Tool and "tabs" to verify the table definition.
I suspect that they are shared.
Sharing of an extension is illustrated in the video 16.
You create a JMS template rule where you select the extension that you want to shared.
www.jms2win.com/en/tutorial#jms12x-16
If the tables are not shared but that you read the content of the master wehsite, perhaps that GroupJive, bypass joomla and proceed with its own stuff to read the DB.
As you ask on how to share, I suppose that the tables are not shared and that there is something in GroupJive that perform direct access to a DB.
Perhaps you could report that to Community Builder