I cannot observe this on my Nexus 9. However I do observe another bug. Whenever the screen orientation changes, the JUCE Demo jumps back to the "Welcome" page, regardless of what tab (the Teapot or anything else) it was previously showing. (Do you have that, too?)
OK! Both issues (teapot being black on rotate and app restarting on rotate) should be fixed on the latest tip. You will need to re-build the Introjucer and re-introjuce your project to pick up the fix.
I've often wondered (but never bothered to find out) - IF I re-introduce a jucer project, MUST I re-import the project under Eclipse/Visual Studio, or can I continue to use the (already started) project?
Under Android Studio you typically have to re-import the gradle file, or at least re-sync with gradle (if you changed some build options). I assume that in eclipse it's similar (although I stayed away from eclipse so far and I'd like to keep it that way ;-).
In Visual Studio typically I can re-introjuce with the solution open. VS will pick up that the project has changed and pop up a dialog box and I just simply click on the reload button.