Is there any reason why you are using tbb::tick_count::now() instead of QDateTime, QTime or QElapsedTimer?
Good question since both are valid platform-portable solutions. The answer is framework portability. I'm intending to implement the entire game engine/logic as a decoupled module from the GUI/Qt framework so that I can just plug it into other frameworks more easily, such as SDL, Glut, or any other kits. I could just say: gameInstance->DoFrame(); from within OnIdle() function, which I assume in this case, works exactly like a idle event block in conventional win32 api non-blocking GetMessage even loop.

Now my question, is there any strong argument why I should not use any other 3rd party libraries in Qt?

Furthermore processing events from within the call to OnIdle() (which I assume is the result of the timer's timeout) doesn't make any sense since the events has just been processed.
pApp->processEvents() was suggested by someone for solving the same issue, but it was a different thread.