The reward is a choice. First he can return to his world and his lovely family but this alexis world will be detroy is he choose to going home to his original world. Second he stay at this alexis world and everything will be okay he can be with alexis family and be happy with him but he will never his original family ever again since he can't go back to his original world.
Eugene our mc need to choose between that, this is why he is crying until his fever got high and sleep all day. He think it's isn't fair at all. He got fond with alexis family but he missed his mom alot and he want to go back but he know he will never survive with the guilt of destroying alexis world. This novel is more details describing how Eugene feel, i actually kinda disappointed they just rushed it but it's as expected since it's a manhwa. I actually cry with Eugene when he feel unfair that's that reward turn out like that. After everything he done that's what he will get? So unfair. He deserves meeting his mom and his family seriously
New chapter
So what are the rewards and penalties? I don't get it