And what season is that from? I'm guessing Season 1 because Paul is not the Chief Engineer. It has been openly said that he's not the chief engineer. So clearly plans changed somewhere between season 1 and 2. It doesn't even make any sense for him to be chief engineer in the first place. He is an astromycologist.
Edit: It was a production mistake. He isn't Chief Engineer.
A graphic seen in "Choose Your Pain" referred to Stamets as the chief engineer, but Ted Sullivan discarded this as a production mistake, quipping, "I'd say he's the chief engineer of spore drive but not of engineering."
Ted is a producer of the show.