You are correct with your educated guess. The ethnic group predominantly living in Adi Urgi (now known as Mendefera, which means "who dares") is Tigrinya ethnic group and has been that way for a long, long time.
Archaeological evidence seems to indicate the ancestors of Tigrinya people have been living in the Eritrean highlands (including Adi Ugri/Mendefera) for at least 2,900 years.
You can read more on it here: http://news.bbc.co.uk/2/hi/africa/2000297.stm
Tigrinya ethnic group represent 55% of the population
Tigre ethnic group represents 30% of the population
The rest 15% are split among Saho, Afars, Beja, Bilen, Kunama, Nara and Rashaida.
Thank you for the excellent information! But this is where my own confusion now comes in... I'm assuming these DNA tests are too broad and general; maybe not very accurate (I have thus far taken the Ancestry test, will be doing the 23andMe test next) because for my mother's side it shows that I am 15% Greek/Italian (they consider Greeks and Italians the same thing) 24% "Middle East" which can include Saudi Arabia, Iran, Iraq, UAE, Syria, Jordan, etc. and 6% Cameroon/Congo.
So I was assuming that the Tigrinya people, if you go far enough back, are actually Arab/Congolese mix? Where the Arabs migrated down into Eritrea while the peoples from the Congo were migrating up to Northern Africa? In any case, I will be getting a "second opinion" when I do the other DNA test soon... but I do encourage everyone to do a DNA test, as you just might be surprised at what you find! (We were always told my Father was Irish and Scottish, the DNA test says mostly Irish and Scandinavian instead, which makes sense, since the Scottish were made up of Celtic/Irish and Scandinavian people.)