The Ivory Coast international joined Spurs for £23m during the summer transfer window from French giants Paris Saint-Germain.
However, the deal was almost scuppered by problems over a work permit which stemmed from his conviction for assaulting a police officer outside a nightclub in Paris last year.
The 24-year-old has also previously been banned by PSG for directing homophobic language at then-manager Laurent Blanc.
Speaking after his side's 3-2 win over West Ham United, in which Aurier was sent off after two yellows within minutes of each other, Pochettino revealed that the defender's reputation has not been a problem.
"His reputation is not about getting sent off many times," the Spurs boss is quoted by the Evening Standard as saying. "His behaviour is fantastic on the team, since he arrived.
"The teammates love him. He is a very good teammate and he is very good friends with Kieran Trippier, who he competes with for the same position.
"I think, to be honest, he is doing very well. We are so happy with him."
Saturday's result at the London Stadium puts Spurs fourth in the Premier League table.