I suppose that we (human) do not read correctly the information that we see.
If you tell me that the JMS Tools show you table and that you don't see them when you connect with PHPMyAdmin, this mean that we do not read the info correctly or that JMS is connected on something else that would explain that with your PHPMyAdmin, you would not be connected where JMS is connected.
So we have to read again and try identifying the reason.
If you want that I have a look directly on your environment, this is still possible with our billable support that you can buy at
www.jms2win.com/en/joomla-multisite?page...35&category_id=1