Albert Barnes 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)

This is the first time that the “house of Joseph,” or simply “Joseph,” is used to represent all the ten tribes which Ephraim led. While Saul of Benjamin was king, or while Mahanaim was the capital of his son’s kingdom, it was not natural to name them this way, nor does it seem natural at first glance coming from Shimei the Benjamite. It is very possible, however, that he used the phrase to exonerate himself and his own tribe from initiating the rebellion, insinuating that they were drawn away by the overwhelming influence of the great house of Joseph.

On the other hand, the phrase may indicate that the passage was written after the separation of the kingdom of Israel, when this expression had become common.