Charles Ellicott Commentary 2 Samuel 19:20

"For thy servant doth know that I have sinned: therefore, behold, I am come this day the first of all the house of Joseph to go down to meet my lord the king." — 2 Samuel 19:20 (ASV)

The house of Joseph. —Shimei was not strictly of “the house of Joseph,” but of Benjamin; and it is plain that Joseph, as the name of the most prominent member, stands for all the tribes outside of Judah. This usage is well recognised at a later time (see 1 Chronicles 5:1–2; Amos 5:15), and it has therefore been argued that it indicates a late date for the composition of the book; but it is also found in Psalms 80:1-2; Psalms 81:5 (the date of which it would be rash to attempt to fix), in the reign of Solomon, 1 Kings 11:28, and probably very early in Judges 1:35.

There is no reason why the expression may not have been used at the earliest date when there began to be a certain separation and distinction between Judah and the other tribes, which was soon after the conquest of Canaan.