Barcelona splashed out a then-club-record fee which could rise to £135m on Dembele last summer following the departure of Neymar to Paris Saint-Germain.
But the winger endured a hugely frustrating start to life at the Nou Camp as injury prevented him from making an impact under Valverde.
Philippe Coutinho’s superseded Dembele as Barcelona’s most expensive signing ever in January, a deal which also provided more competition for him.
Dembele was linked with a move away from Spain over the summer, with Premier League giants Arsenal and Liverpool both thought to be keen on him.
However, the former Borussia Dortmund wideman ended up staying put and he has started all three games of the new season.
Dembele will be keen to shine on Saturday when Barcelona return to La Liga action after the international break.
And Valverde is demanding the 21-year-old delivers on a regular basis, with a host of players ready to step into his shoes if not.
“He’s the same player [as the one Barcelona signed],” Valverde said.
“He’s great going forward, great at finding space, he scores goals.
“We also want consistency from him.
“He’s working very hard in training but essentially he is the same player.
“There will be big games when we need him to rise to the occasion, but that’s his job.”
Dembele will be buoyed by having played a role in France’s World Cup win earlier this summer.
And against Sociedad he will be looking to add to the two goals he’s scored so far this term.
Dembele notched the winner against Real Valladolid and bagged in the 8-2 thrashing of Huesca.
And Barcelona are out to extend their unbeaten run against Sociedad, alongside their 100 per cent start to the La Liga season, on Saturday.