タイッツー is definitely taittsuu. Twitter doesn’t seem to use a katakana spelling. Your proposal of “tsuittaa” would be ツイッター. Same katakana but different order. There would be no reason to read Japanese from right to left. Might be an intentional pun though.
Edit: it’s https://taittsuu.com/
36 / M / Germany
Pretty much spot on.