Well, when the Judahites (the descendants of Jacob that inhabited the regions marked out for the descendants of Judah and Benjamin) were carried away to Babylon for more than 70 years, they remembered the promise from the prophets of God that they would return to inherit the land that He had promised Abraham.
As a practical matter, but also because they believed the Promise (the Abrahamic covenant), their scribes kept genealogical records of the families in captivity. We know this from the scriptures recording their return from exile. The precise number of each returning family group returned to the very town or rural area from which they were removed is recorded in 2 Ezra, Chapter 2 (Orthodox Study Bible). No doubt when the ancestors of Anna had returned from the Babylonian-Persian captivity, they went back to the lands that they had occupied in Judea.
However, there remains a question as to why anyone from the tribe of Asher would be included among the Judeo-Benjamites, because Asher, the son of Jacob, had been assigned lands in the regions that became known as the Northern Kingdom (Israel as opposed to Judah, the Southern Kingdom). Sennacherib, King of the Assyrians, ethnically cleansed the Northern Kingdom, about 725 BC. (4 Kingdoms, Chapter 17, Orthodox Study Bible)
This would have meant that all the descendants of Asher could have disappeared with the rest of the Ten Lost Tribes. But instead we find that Phanuel, father of the Prophetess Anna, has survived the Assyrian genocide, the Babylonian Captivity of Judah, and begets a daughter in Jerusalem just about 84 years BC.
This means we have to search out the tribal history of Asher, the son of Jacob (Israel). So we must trace the tribal movements from Jacob to at least the time of the Return from the Babylonian Exile.