Alma’s House is Alma’s own house in the land of Zarahemla. Alma came to Zarahemla with Amulek and “took him to his own house” after seeing the events involving Amulek (Alma 15:18).
Alma “did administer unto him in his tribulations” and “strengthened him in the Lord” at his house (Alma 15:18). Amulek had been rejected by former friends, his father, and his kindred (Alma 15:16).