Walters scored twice in the Potters' 3-0 victory at West Brom on Saturday, taking his tally with his new club to four goals in all competitions.
Having previously spent his career playing in the lower leagues, the striker - who also won his first cap for the Republic of Ireland last week - has so far adapted well to a higher level.
Pulis could see the potential in Walters to make that step up and the manager is pleased the 27-year-old has also made his mark in the other way he hoped - in the dressing room and on the training ground.
"Jon has not just been bought in respect of what he is going to do in the first team," Pulis said. "He has also been bought as a player who will mix in with the group and his attitude and commitment to everything he does, both on and off the pitch, is absolutely first-class.
"The players have really taken to him. We have a good spirit at the football club and the secret is to try and maintain that spirit and togetherness. Jon has moulded in so well. Obviously we are delighted he has got four goals already this season, but it's also his application and attitude around the place. As a lad, he has really mixed in and grown with the group."