Unfortunately that article talks about "staggered isometric" rendering, which is a different kind of isometric that Tiled uses.

You may want to look at the code from Tiled Java that implements the isometric rendering, and see if you can adapt it to render the maps in your game:

http://tiled.hg.sourceforge.net/hgweb/tiled/tiled/file/0.7/src/tiled/view/IsoMapView.java

Eventually I also hope to include isometric rendering in libtiled-java, which is a small TMX support library shipped with the current Qt version of Tiled. It's not a priority for me though, but maybe somebody would like to work on a patch for that. :-)