You(and we) can not pronounce"タ三ア". "三" is kanji(Chinese character) means "three". "三" should be "ミ"(katakana). Then you(and we) can pronounce"タミア<tamia>". Young Buddhist priests took basically a part of the kanji and used it as a phonogram in order to write down quickly lecture of teacher in 9th century. In most, on-yomi<a sound reading＝Chinese pronunciation> was used, but there are several katakana that kun-yomi<the Japanese reading＝Japanese translation> was used. ミ<mi> is one of them. The letterform of "ミ" has come from "三". "この　子　が／は　タミア。" means "This child is Tamia".

み is a kun'yomi reading for the Kanji 三, so yes, that could be pronounced tamia

Everything you said in your question is correct. The romanji for the sentence is "kono ko ga Tamia" For foreign words or names they use the katakana alphabet; the characters in Tamia are katakana. The rest is the hiragana alphabet, except for ko, which is kanji.