Martinez's Wigan sides were renowned for an attacking approach during his spell in charge at the DW Stadium
The French defender can see some of that philosophy in action with the Toffees, but he insists that the fundamentals of his department are being adhered to.
"If the manager asks me to play long, I play long. If he asks me to play short, I play short. If I have to run around and tackle, I tackle! I don't think, as a defender, there is a lot of difference," Distin told Sky Sports News.
"He just encourages us to play a little bit more football, and start from the back. No matter the manager, defending is always the same.
"It's a different regime, a different style of training and a different way of speaking to the players. You just have to adapt and you get used to it quite quickly, it's not difficult."
However Distin is tipping Manchester United for immediate success under his former Goodison Park boss David Moyes.
"They are the most consistent team in the past 10 years, they are always there, no matter what," added the 35-year-old centre-back.
"They always finish in the top two. It's an amazing team, they have the experience, and they have everything to win the title again."