Share the same user base between the master and the slave site does NOT mean to share the whole website content.

To share a whole website, you need to share the same DB and same table prefix.

In tutorial video 16, it is explained how to share the users between websites.
You can do the same to share the users between the master and the slave site.
www.jms2win.com/en/tutorial#jms12x-16

This will share the users and not everything.
So you can have different articles, menu, .... specific in each websites.
Only the jooml users will be shared.

Concerning the original question, can you check in your browser if you have javascript error that is returned.
Check also if you have a "error log" that would report an error message that could help identifying the reason of the partial rendering.

Also try to install JMS 1.2.71 to see if that solve the issue.