Kone put pen to paper on a five-year deal worth £90,000-per-week just eight months after joining the Black Cats from Lorient for £6m.
Having met his demands, Moyes says its payback time for the Ivory Coast international.
“He had a contract promised to him and the club were always going to uphold that," said the Scot.
“Lamine has now gone to a level where he has to become a leader and top player for us.
“His contract suggests that and we now need him to perform at a really high level."