There are several methods of romanising Japanese.
http://en.wikipedia.org/wiki/Romanizati ... ihon-shiki
The Hepburn system is the most widely used outside Japan. (chi, tsu, shi)
The version in use on the katakana / hiragana section sounds like Kunrei-shiki, the official system in Japan. Which predates IMEs by the way, unless you count manual QWERTY typewriters. When I have had Japanese people write to me in romanised Japanese they have very different ideas about romanisation and word breaks.
If I have to romanise Japanese I prefer the simpler and more consistent ti, tu, si etc.
I suppose the important thing is to be consistent with how you romanise and use a system suitable to your audience.
But it ought to be trivial for a program to accept either version as being correct, and given that this is a site for JSL learners Hepburn ought to be included really.