Martinez, having goaded France fans and players after Argentina's World Cup triumph, is facing a backlash from PSG fans for their Champions League quarterfinal first-leg.
"He is mature. He is responsible. He is getting better at controlling his emotions. He is a better goalkeeper than he was when he joined Villa in 2020," said Emery.
"Now my conversations with him are the same – focus on football, on your individual challenges, and try to manage everything you are achieving. Try to control the emotion it is bringing to you."
Villa teammate Youri Tielemans also said: "I don’t care about it – we are here to play the game and I don’t mind whatever happens with Emi as long as it stays respectful in football terms.
"That is probably his style. He is ready for the game and hasn’t spoken differently to us from how he does before any other game. He is focused and looking forward to it."
Martinez certainly wasn't hiding yesterday, as he touched down in Paris with the squad wearing a cap sporting the four titles he's won with Argentina.