If I remember from the novel, Eugene eventually left the castle and told himself that he won't like Alexis anymore as he don't want to stay with someone who does not like him. Alexis really hates prophets or those who can see the future and he's afraid he might harm Eugene (tho he knows he won't be able to harm him)
Alexis actually followed Eugene as he thought Dagona will be helping him. Eugene was like "I thought you wouldn't see me? Why did you follow me". He wants to explain that he is not the real Lord Eugene but of course the system would not let him and he coughed blood, so he just told Alexis to not like him. Alexis misunderstood and thought Eugene was just using him for personal gains. He really wants to tell Alexis his secret :((
Anyway so he told Alexis to stop liking him and he won't like him anymore as well. He can't help by cry as he was really frustrated of their situation and Alexis was like "I'll take my wife back". They actually went back together, I think Eugene loose consciousness and had a fever again. Alexis had the time to think how regretful his actions were towards Eugene. I think there was a scene after that he apologized and just smiled bitterly when Eugene told him again to stop liking him.
I'm excited for how things would work in webtoon ~
PS. They will reconcile don't worry. I look forward to their kisses XDD