The Welsh defender has had to adapt quickly to the Dutchman's methods.
Everton manager Ronaldo Koeman
The defender is one of four new signings at Goodison Park this summer, having arrived in a deal from Swansea City earlier this month.
He was brought to the club as a direct replacement for John Stones, who completed a protracted big-money move to Manchester City the day before Williams' arrival.
Everton's Ashley Williams applauding fans as he is paraded before the match
The Welsh international arrives at the club in a time of change, with new ownership and a new manager, Koeman, looking to guide the Blues into a new era.
To do so will require hard work on and off the pitch and Williams has provided an insight into what training is like under the Dutchman.
“Training has been different to what I’m used to,” he told the Daily Mail.
“It’s very intense and makes you think a lot as well. All the boys are working hard and trying to impress him to get into the team or stay in the team.”
Everton's Ashley Williams being paraded before the match
It is no surprise to hear of Everton’s training sessions being intense given Ronald Koeman’s complaints about his side’s fitness already.
He has claimed his team is only 70% ready for the beginning of the campaign, and that was noticeable on the opening day as they visibly waned in the second half against Tottenham Hotspur.
That is obviously a situation that needs rectifying, and it is easy to imagine that training will remain intense for some time yet.
Everton manager Ronald Koeman