Anna of the tribe of Asher being counted within the house of Judah (Judah, Benjamin, Levi) is explained during the split of the two houses of Israel in Solomon's days.
IKing 12:16-21
16 So when all Israel saw that the king hearkened not unto them, the people answered the king, saying, What portion have we in David? neither have we inheritance in the son of Jesse: to your tents, O Israel: now see to thine own house, David. So Israel departed unto their tents.
17 But as for the children of Israel which dwelt in the cities of Judah, Rehoboam reigned over them.
18 Then king Rehoboam sent Adoram, who was over the tribute; and all Israel stoned him with stones, that he died. Therefore king Rehoboam made speed to get him up to his chariot, to flee to Jerusalem.
19 So Israel rebelled against the house of David unto this day.
20 And it came to pass, when all Israel heard that Jeroboam was come again, that they sent and called him unto the congregation, and made him king over all Israel: there was none that followed the house of David, but the tribe of Judah only.
21 And when Rehoboam was come to Jerusalem, he assembled all the house of Judah, with the tribe of Benjamin, an hundred and fourscore thousand chosen men, which were warriors, to fight against the house of Israel, to bring the kingdom again to Rehoboam the son of Solomon.
(KJV)
When God gave Jeroboam of the house of Joseph to become king over ten tribes of Israel in 1 Kings 11, the above shows some remnants of the ten tribes were already living south in Judea around Jerusalem. Thus a few of any of the ten tribes no doubt decided to stay in Judea and thus became under the "house of Judah", and even later became known as Jews also. But per God's Word at the split, that would have been a small number out of the ten tribes, the majority staying in the northern kingdom under king Jeroboam of Ephraim.