First, I'd like to verify that your problem is with regards to the studio (used for modeling/development - based on eclipse, does not require tomcat to be installed) and not the standalone server (used for deployment - based on tomcat).
I assume you've followed the Tersus Studio - Cross Platform installation instructions, and while installation seems to have been successful (i.e. you are able to access the sample application models), when you open the embedded application server (Application Sever view) it is empty.
I would suggest the following:
1. Try to refresh the application server view (by pressing the Refresh button on the view's toolbar)
2. Using the Repository Explorer view, verify that in any of the missing application, there is a Package which has a name identical to the name of the application, and that the package contains a System element whose name is identical as well. Also verify, in the Navigator view, that there is no Configuration.xml file in the application.
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