Back in January, Puncheon's future looked uncertain as he was cast out of the Saints first-team squad and forced to train with the reserves.
At the time the 26-year-old insisted his exile was caused by Cortese rather than manager Nigel Adkins, but now he is convinced talks with the chairman have resolved any long-standing issues.
"Me and him had clear-the-air talks and, as far as I'm concerned, that's all history," Puncheon told the Sun.
"I am just pleased to get the chance to keep producing.
"It is all about growing and maturing as an adult and a player and I am doing that.
|THE SAINTS GO MARCHING DOWN
|6/1||Southampton are 6/1 with Bet365 to finish bottom|
"The gaffer has given me a platform; given me a chance and I have grasped it with both hands.” he continued.
"That is what has happened and that is why we are where we are. There are a lot of differences now. It is massive playing in the Premier League.
"I am getting the chance to play football, that is the most important thing as far as I am concerned."