How were the additional words in some readings written in the Uthmanic Mus'haf, despite the variations in readings, and does their presence mean a violation of the Uthmanic Mus'haf?

The confusion stems from the questioner's understanding that Uthman ordered the writing of only one Mushaf, and thus there could be no variations in the multiply transmitted (mutawatir) readings. The correct understanding is that Uthman ordered the writing of several copies of the Mushaf, which were sent to various regions (amsar), and these copies included confined and documented variations.

For a reading to be valid, it must conform to the orthography of one of the Uthmani copies of the Mushaf. There is disagreement regarding the exact number of these copies, but the most well-known opinions are four and seven. The copy that Uthman kept for himself was called "Al-Mushaf Al-Imam," and sometimes this name is used to refer to all the copied and dispatched Mushafs.

Some Quranic words in the Uthmani Mushafs were written with more than one form to accommodate different readings. The reason for this slight variation is that the Companions wrote down what they were certain was the Quran and what had been established in the final recitation (al-ardah al-akhira). There were indeed differences between Uthman's personal Mushaf and the other copies, and these differences are confined and well-known.