The talented Ivorian right-back joined Spurs for £23 million ($30 million, 25 million euros) from PSG on transfer deadline day last week.
The deal was held up as Spurs’ request for a work permit was complicated by the suspended two-month prison sentence Aurier received after an assault on a police officer outside a Paris nightclub in May 2016.
The 24-year-old was also suspended by PSG last year for making a homophobic slur against former coach Laurent Blanc in a social media video.
Pochettino, whose comments were published in the British press on Friday, is a strong disciplinarian and insists he will come down hard on Aurier if he steps out of line.
“I said to him, ‘I will kill you’, I (would) head-butt him,” Pochettino said.
“I think it was good, we had a long chat. He knows very well how we are, what we expect from him and for us it’s so important, not only him, every player, how they behave here in the squad.
“We need to keep the dynamic we have created. I trust him, I am confident that he can succeed here and help the team to achieve the things we want.
“When you know and you meet some people, always you start to assess him from the day that you meet them and for me we start from (here) because I don’t know him before. For him I think it’s a new chapter in his life.”
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