Tbh, I think it depends on who writes it but, I noticed that it was always omegas that they'd take in, probably if it is between omegas then that's a difference case? XD most of the time this "sickness" would be shown if another alpha forced a bitten omega to have sex owo but who knows, maybe on this one is slightly different. (づ ̄ ³ ̄)づ still glad they're all happy now.
As far as I know that's only the case during their heat.
When the bitten omega's in heat and another alpha/beta/omega tries to have sex with said omega, it would result in vomiting/sickness in general. Outside of heat nothing happens....but I may be wrong OoO
In Remnant, they would still get sick outside of heat. This could be author preference. However, Ai no Makoto is linked with Romantic Joutou universe wherein omegas get sick when having sex with someone not their mate in/out of heat. So.
Either there's a special omega to omega magic. Or. He doesn't get sick because Seiji is there too.
I thought omegas who have been bitten get sick if they have sex with other people who aren't their mates.