Vunipola's first England start in Montevideo came the day after his elder brother, Mako, and his cousin Toby Faletau had made their debuts for the British and Irish Lions in Hong Kong.
"I spoke to my brother on Friday night and I just said good luck to him. I am really happy for him and Toby to be playing," Vunipola said after England's seven-try win. "He texted me saying 'good luck, concentrate on the things I do well like carrying the ball and not get overawed by the occasion of playing for England for the first time'."
He added: "I have never scored a hat-trick. Maybe I did in school - but school is a bit easier than international rugby.
"Personally I thought I went OK, but nothing exceptional. I will tell him I did OK, I don't want to blow my own trumpet."
Vunipola's hat-trick, two of which were scored from driving lineouts and the third after some sharp build-up play from Kyle Eastmond and Jonny May, sealed England the win.
But head coach Stuart Lancaster admitted the Red Rose were given a valuable wake-up call ahead of the forthcoming two-Test series against Argentina.
On top of Vunipola's hat-trick, Ben Foden scored twice and there were tries from captain Tom Wood and Paul Doran-Jones as England came from behind to win.
But the CONSUR XV - comprised of players from Argentina, Uruguay, Brazil and Chile - dominated the first and last quarters of the match.
"As a team we need to go back to the drawing board and try to work on the fundamentals - the ruck and the tackle area - because Argentina will come at us hard there. We slipped off a few," Vunipola said. "That will be the biggest challenge for us."
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