The 24-year-old arrived from Brentford for a club-record £28million fee, which could rise to £33m, and that immediately had critics questioning whether he could cope in the top flight.
Watkins has scored eight times in 10 all competitions so far, including six in his last five Premier League games with a hat-trick against defending champions Liverpool and two against Arsenal last time out.
“If you speak to Ollie he won't care who he scores against and I'm pretty much the same to be honest," said Smith, who originally signed the striker for Brentford in July 2017.
“You want your number nine to come in and score goals and he's certainly done that.
“He has a hunger to score goals, which is what I love about him, he has a hunger to improve and keep getting better and what you see on a match day is what you see on the training ground.
“I had no doubts – he had scored 25 goals in the Championship last season – he would come and not replicate 25 goals but replicate scoring and he has shown that already and will continue to do that."
When Smith signed Watkins for Brentford he bought him a fish tank – with disastrous results – but having been successfully reunited he believes a gift is due from the striker.
“I used to go and visit the players I signed at Brentford, pretty much to have a spy on how they were living without them knowing so I used to take them a little present," he added.
“I took Ollie Watkins a fish tank but he didn't keep the fish too well and they didn't last very long unfortunately. I don't think he fed them often enough.
“He should be buying me something now. I've done my bit for him, he should be buying me something."