I upgraded to Java 1.7.0_45 and that solved the offset problem. The JME canvas now draws within the tab. However, it always remains at the forefront. The canvas is on the first tab and when I switch to the second tab the canvas remains visible, obscuring what’s in the second tab.
Might be LWJGL canvas not properly responding to being obscured.
You could try placing some Swing widget (JPanel recommended, less optimizations that might interfere) in the glass pane of the top-level window. The glass pane is always in front of the normal stuff, so the JPanel should remain visible no matter what; if the canvas overdraws it, they did something wrong.