I observed that links to other domains within TYPO3 were not setting the URL properly. A link from ITS to ITSECURITY was being generated with the ITS URL and as a result didn't work.
So I added the following lines to the template and observed that the correct URL is now used. It is not using RealURL, but this seems to be a known bug ( http://bugs.typo3.org/view.php?id=3491 ) so I will keep an eye on it for a more beautiful solution.
# allegedly is supposed to make links between domains work
config.typolinkCheckRootline = 1