McCarthy enjoyed a fine debut season in the heart of Everton's midfield, after manager Roberto Martinez paid an estimated £13 million to former club Wigan Athletic for the Republic of Ireland international last September.
The 23-year-old was one of a host of deals that Everton completed, with the likes of Romelu Lukaku and Gareth Garry also making the switch to Goodison Park on loan deals.
However, Everton assistant Jones believes that McCarthy more than any other signing faced the most pressure because he played under Martinez at the DW Stadium.
But Jones, who first came into contact with McCarthy during his time as a player and coach at Hamilton Academical, had no doubt that he would make a seamless transition and hailed his consistent performances.
"He has been like that since I met him at 15," Jones told Everton's official website "I'm not kidding you – anybody who knows him knows he is so consistent as a human being. He loves his football.
"When you go to a football club as a management team there's always one player who always gets identified with that management team. We had it at Wigan initially with Jordi Gomez and then here with James McCarthy.
"The pressure is on that player more than any other signing because they have come from your former club. He's had to get through those hurdles first and then he has gone from strength to strength after that.
"So it's not been easy for James. Out of all the signings, he's had the most difficult challenge and he has come through that no problem."
Jones also stated his belief that McCarthy has drastically improved the tactical side of his game, something he credits Martinez for.
He added: "If you check his (McCarthy's) record, he is closing in on 300 games already and he is only 23 years old. This is not a guy who at 23 is not experienced. Physically and technically he always had that ability.
"We took him to Wigan with us and the manager has to take a huge pat on the back for the tactical aspect that he has given James. Every other area he had but I think the gaffer, being a former midfield player, has taken James to another level."
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