Amulek gave the exact day, month and year for the arrival of the angel: "The fourth day of this seventh month, which is in the tenth year of the reign of the judges" (10:6). Why is such detail given? He even stated that he was going to visit a "very near kindred" (Alma 10:7).
In the Law of Moses, doing things precisely on certain days and months was crucial. When the law said that you shall do something—such as the observance of Passover, the Feast of Tabernacles, or the Day of Atonement—it declared specifically on which day it should be. Thus, the day, month, and year were extremely important to the children of Israel, and we can assume that the Nephite calendar followed the Law of Moses.
The first month of the year for the pre-exilic Israelite calendar was in September. In the "commencement" of the new year, Rosh Hashanah occurred on the first day of the month. The Day of Atonement and the Feast of Tabernacles followed, all within the first month of the year. The other large festival, Passover, was seven months later. As Amulek relates it, on the fourth day of the seventh month, he is traveling to be with his family, or "very near kindred."
What kind of a festival was Passover? It was when the family gathered, sacrificed the lamb, and had the Passover meal. They set a plate for the coming of the Prophet Elijah, expecting that one day he would return. One wonders, in that connection, what Amulek thought when the angel said, in effect, Go home, have Passover there, "for thou shalt feed a prophet of the Lord" (10:7).
Passover also commemorates the time when the destroying angel passed over the homes of the Israelites in Egypt and spared those who had the blood over their door. The coming of an angel was a large part of what would have been remembered and included in the Passover celebration.
After Alma had finished giving his first judgment speech against the people in Ammonihah, the people tried to arrest him and put him in jail (9:33), but with the Lord’s help he evaded their attempt. As he was on his way to the city of Aaron, the same angel who had converted Alma (8:15) told him to "return to the city of Ammonihah" and preach there again (8:16). As Alma reentered the city, he met Amulek as he was returning back to his home (8:20; 10:8). Amulek took him to his home, even though he likely knew what Alma had said to the city and had been rejected and was considered a criminal. So Amulek put his own social status on the line by talking to Alma and receiving him, who was hungry from fasting for many days and was "a holy man, who is a chosen man of God" (10:7), and of this Amulek could truly testify.
When Alma spoke those fateful words, "Will ye give to an humble servant of God something to eat?" (8:19), what a manifestation that must have been for Amulek! And with that, Amulek, together with his women (likely his wife, mother, and maybe sisters), his children, his father, and his whole household, were blessed and were tutored by Alma and became converted (10:11). They were blessed by having received a prophet, for "he that receiveth a prophet in the name of a prophet shall receive a prophet’s reward" (Matthew 10:41).
Welch, John W. Welch, "The Trial of Alma and Amulek," in The Legal Cases in the Book of Mormon (Provo, UT: BYU Press, 2008), 237–271. "Although the visitor turned out not to be Elijah coming before ‘the great and dreadful day of the Lord’ (Malachi 4:5), Alma did come to announce the day of destruction in the city of Ammonihah, with the destroying angel passing over only [a] few [of those] in that land who were willing to receive Alma’s message" (p. 240).
Book of Mormon Central, "Were Nephite Prophets Familiar with the Passover Tradition? (Mosiah 13:30)," KnoWhy 420 (March 29, 2018).