@Me A Fangirl I think he did, that's he why asked all those things like if Eugene will stay alive if they swapped again and if he will live etc. He also said before that, "how do you expect me not to be swayed?" while crying. He wanted to stay with Alexis but also misses his family.
But Yujin is also a good guy, he couldn't possibly let OG Eugene die after he saw OG Eugene's happiness in his flashback. Most importantly, he just loves Alexis too much to leave him.