Pochettino has settled well at St Mary's after replacing Nigel Adkins in January.
Puncheon admitted: "When he first came I knew him mainly as the guy who gave away the penalty for Argentina against England at the 2002 World Cup.
"But he's a good man at heart and his knowledge of the game is immense. His English is getting better all the time as well and he speaks to the boys directly, even if he still uses an interpreter for interviews.
"He's always joking and starting to join the banter."