Steven Naismith assesses his progress in small measures.

There was his 20-minute outing in Everton's friendly against Motherwell, a hat-trick in another friendly against AEK Athens, then playing the full 90 minutes of Scotland's friendly victory over Australia last Wednesday night. "Just getting to kick the ball again in pre-season was great," he says with a tentative smile.

The caution is obligatory. Last October, he damaged the anterior cruciate ligament in his right knee, having suffered a similar injury to his left knee three years before. After the rehab for his first injury, Naismith felt it took a further six months to return to his accustomed form and assurance. Now, strong, confident, forceful, he already feels capable of the dynamism that is the hallmark of his game.

The hat-trick for Everton against AEK was scored in the space of 30 minutes, and the sense was of a player already attuned to his new surroundings. There was a steeliness to Naismith when he revealed, at a press conference he arranged himself with former team-mate Steven Whittaker, his reasons for leaving Rangers during the summer. Some Ibrox fans will always consider it a betrayal – not least because Naismith remains an avid fan of the club he grew up supporting in Ayrshire – but this was a player taking firm control of the circumstances he faced.

Naismith felt let down by Craig Whyte, then the administrators, then the new owners, a consortium led by Charles Green. With two serious knee injuries in his past, and a grievance, he chose not to allow his contract to be transferred to the company set up by Green to acquire the business and assets of Rangers, and so effectively left on a free transfer. "There are days when [recovering from injury] is really tough but you have just got to grind through them and there were obviously a lot of other things going on as well, which took my mind off the injury for a wee bit," Naismith says.

The move to Everton seems a perfect fit for Naismith. He could, already, be the archetypal David Moyes player: industrious, clever, ambitious, disciplined, undaunted. Following the hat-trick against AEK, Everton fans are proclaiming Naismith as the heir to their last icon, Tim Cahill, Moyes had to caution against heightened expectations. The comments would have been pointed, but not unreserved; Moyes himself will demand a high level of performance from a player who in the early months of last season was out-performing everybody else in Scotland.

"I had a good chat with him and he was saying all the right things and other people I spoke to said he wants you to work hard and that's the kind of trainer I am, I want everybody to be working at their best," Naismith says of his new manager. "He is thorough with what he does and he plays a certain way and wants everybody to work for each other, all the things I like as a player. He definitely doesn't leave a stone unturned. From him and all the coaches, there is a real good feeling throughout the squad and they are always telling you things you can improve on and praising you when you need to be praised."

Everton's opening league game of the season is against Manchester United at Goodison tomorrow night. Naismith considers himself fit enough to play, but Moyes has yet to decide if the 25-year-old has returned to the peak condition required for the cut and thrust of the Barclay's Premier League. Naismith is diminished when not at his most athletic, but he does not suffer from an inferiority complex despite the demands of his new environment.

"The squad is full of quality players and part of my decision was that the squad wasn't too big that I wasn't going to get my chance," Naismith says. "That played a big part. With better players you're going to become a better player yourself and, hopefully, training with these boys every day will make me better. From defence right through to attack there is real quality, but hopefully I can produce in Premier League games and score goals. It's something I have enjoyed doing throughout my career and Everton will be no different."

Naismith took several months to adjust to the expectations at Ibrox, but he is older now, more hardened to the assumption that a player has to rise to the occasion, whatever the circumstances.