Right now, I see two issues with Jesse and the 2nd one of them can be "newness" to Carolina.
1) He's not as strong on the puck as you'd expect. He's big, skates well and likes to be physical, but loses the puck more than you'd expect in a battles on the boards even against smaller guys and/or does't come away cleanly with the puck. Not sure if if it's just balance, lower body strength, hands or what.
2) He makes plays that are "simple" plays even when they aren't necessarily the right play. He'll be behind the net and throw it in front even if nobody is there or there's too many players from the other team there vs. holding onto it to make a play. He'll rush a pass or shot, even if it's not there or he can't get much on it, etc. This could be that he's still running on adrenaline or not comfortable in the Canes system yet though, but the game needs to "slow down" for him so he can make the right play based on how things have progressed. Confidence might play a role.
He does a lot of other things fairly well though. Skates well, works hard along the boards, uses his body, works hard and is responsible defensively and has found some soft spots to get some decent shots off.
KK started off slowly as well so hopefully he gains confidence over time.