Amulek has likewise received a vision of Alma’s arrival. He knows that Alma is a prophet, and is fully ready to receive him and share food.
Sociological: Most surprisingly, Amulek announces that he is a Nephite. Why would he do this? To understand the implications of Amulek’s declaration, we need to review what it is that he might be saying. First, it is possible that he is declaring that he is Nephite as opposed to Lamanite. In the Book of Mormon we have many times when those two terms are used as polar opposites to divide people into the “us/them” categories. This certainly cannot be the case with Amulek, because he is living in a city that is part of the area that Alma certainly appears to believe is part of the “land” of Zarahemla (which is Nephite). Thus it would be surprising in the extreme for Amulek to declare that he was Nephite/not Lamanite. Certainly Alma would have been able to deduce that fact simply from where Amulek lived.
It is possible that Amulek is using the actual lineal definition of the term. In the greeting he would be declaring that he is of the literal “tribe” of Nephi. This is certainly a possibility, as Alma’s surest introduction into the visited cities would be with direct kin (Sorenson, John L. An Ancient American Setting for the Book of Mormon. FARMS 1985, p. 311), and it is literally true as Amulek declares in Alma 10:3.
The last possibility is that Amulek is declaring a politico-religious orientation. In the context of the story of Ammonihah, this appears to be the most logical reason for the declaration, “I am a Nephite.” Amulek is living in a city that is clearly dominated by the order of Nehor. This was a conflicting politico-religious view with that of the Nephite religion, and as competition, hardly the place where Alma would look for assistance. When Amulek declares that he is a Nephite, he is telling Alma that he follows the same politico-religious world view as Alma, and is therefore an ally amidst the opposition. For Alma, this declaration of similarity in mode of thought would have been of much greater import than a recitation of genealogy, even though it is true. What this tells us, however, is the extent to which Nephite has superceded its meaning as a marker of genealogy. It must be seen as a label for an idea more than a lineage. Since there was a separation in Zarahemla between political and religious, the idea of Nephite would be more heavily marked as a religious meaning than a political one, though there is no escaping the relationship of the two in the ancient world, even in Zarahemla that nominally separated them.