Currently, WRobotPeer saves the offset of the screen it is created for, and then applies the offset to mouseMove() and getRGBPixel() calls.  There is problem with this - the coordinates returned from Component.getLocationOnScreen() are global coordinates, not relative the their screen.  So, it's much more difficult than it needs to be move the mouse to the location of a Component that is not on the primary display.  The situation also makes it difficult or impossible for one codebase to work the same on the three major multi-screen configurations: X11 using Xinerama, X11 without Xinerama, and Windows.

This has been the case since 1.3, when Robot was added.