It says Peter spoke words by which they would be saved. They anticipated the message, had great reverence for the speaker, and accepted his words as God's words with faith. Did your family members do likewise?
The house was devout:
Acts 10:2 KJV
2 A devout man, and one that feared God with all his house,
which gave much alms to the people, and prayed to God always.
The house of Cornelius was told by an angel what was coming:
Acts 10:22 KJV
22 And they said, Cornelius the centurion, a just man, and one that feareth God,
and of good report among all the nation of the Jews, was warned from God by
an holy angel to send for thee into his house, and to hear words of thee.
The angel told them that Peter would speak words to them and those words would save them:
Acts 11:13-14 KJV
13 And he shewed us how he had seen an angel in his house,
which stood and said unto him, Send men to Joppa, and call for Simon, whose surname is Peter;
14 Who shall tell thee words, whereby thou and all thy house shall be saved.
When Cornelius saw Peter, he revered him so much that he fell down to worship him:
Acts 10:25 KJV
25 And as Peter was coming in, Cornelius met him, and fell
down at his feet, and worshipped him.
Cornelius and everyone present knew that the words they were about to hear were commanded by God:
Acts 10:33 KJV
33 Immediately therefore I sent to thee; and thou hast well done that
thou art come. Now therefore are we all here present before God, to
hear all things that are commanded thee of God.
So Cornelius and his house were ready for this, anticipated the coming and the outcome, and were much like the Bereans who heard with similar "nobility"
Acts 17:11-12 KJV
11 These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so.
12 Therefore many of them believed; also of honourable women which were Greeks, and of men, not a few.
Even Jesus had to have the respect of the noble hearer to accomplish God's will:
Matthew 13:54-58 KJV
54 And when he was come into his own country, he taught them in their synagogue, insomuch that they were astonished, and said, Whence hath this man this wisdom, and these mighty works?
55 Is not this the carpenter's son? is not his mother called Mary? and his brethren, James, and Joses, and Simon, and Judas?
56 And his sisters, are they not all with us? Whence then hath this man all these things?
57 And they were offended in him. But Jesus said unto them, A prophet is not without honour, save in his own country, and in his own house.
58 And he did not many mighty works there because of their unbelief.