naaah this better just be his plan to hide Eugene

Unfortunately, no. He does care about Eugene but his hatred, at least at this moment, is higher. Eugene would be so hurt.
Tho, he would regret right away but Eugene was already - fuck it, you dont like me, then i wont like you - and went away with the other girl (ogfl) to complete their mission of saving the world. Alexis would be chasing after him to the point Eugene had to put him to sleep to get away. Eugene got an ability to put Alexis to sleep so he's always threatening Alexis with this ability LOL. Anyway, Alexis, for some time, would just gaze/follow Eugene at a distance.
They would eventually reconcile tho and be lovey-dovey after.