The problem is that Windows opened with the EmbeddedStage as their parent have no native parent window (which would be the Swing-JFrame or SWT-Shell) causing all sorts of misbehavior:
* They can get hidden by the window containing the embedded JavaFX-Scene
* Popups don't move if their parent is moved
* Popups are not hidden if their parent is minimized

If the javafx window is modal and the window is hidden by the native SWT/Swing window (which at least on OS-X is possible) the JavaFX-Scene is blocked and the application looks like it is crashed although it is not