There are many omegaverse that are a bit different but to answer your question. Yes. After being marked, an omega body does reject other people except for their alpha. Such as in chapter 6. His body was showing sign of rejection to the point where Kei slap away Tsugitsugu's hand away involuntarily and vomit when his d*ck was inserted inside him but remember. He was in HEAT. Most of the time the SIGNS of rejection occurs, it's when one is IN heat. Other than that, even if an omega is MARKED and if they are NOT in heat. They CAN have sex with OTHER people.
So chapter 6.5 where they have sex again. Kei wasn't in heat and so they have normal sex. I hope this solve your confusion and I apologize about the rant.
I’m confused. Doesn’t an omegas body reject another’s after being marked??? Why isn’t his body rejecting him anymore?