My girlfriend is Eritrean from Asmara. She told me that in the pre-Mengistu era, people from Tigray were poorer than Eritreans because Asmara was developed. As a result, villagers from Tigray used to be travel to Eritrea as seasonal migrant workers (maids, labor work, etc.). This lead to the belief in the Asmarino mind that the people from Tigray were inferior and the word used was "Agame" (as in these poor villagers came from this other place that is inferior to Asmara). So yes, it's similar to how "Chinaman" was used way back when in the US since some poor Chinese workers migrated to build the American railroad.

My mother told me that "Adgi" (translated to "Donkey") was used by Asmarinos to label Gondere villagers.