They do give them pills to prevent pregnancy like birth control. The guard mentioned it earlier they give it to them when it's time or get closer for their heat/rut. He received the pill during his heat with the alpha( who he thought was omega) but since he thought he was an omega and the sex was good he started sneaking around having sex with him. Which lead to the the pregnancy. He didn't find out he was an alpha until he got pregnant.
He wasn't sneaking around though?? He literally put his name down for them to be placed together during his heat. The point is that if majority of this fictional population uses pills for their heats and ruts anyways, it's stupid to let 2 inmates mate together just because of heats/ruts when it can be controlled without this kind of contact
They were and he was provided the pills he even told the MC don't tell his baby Daddy that he thought he was an omega all along. From every omegaverse story I read have they have the same gist taking excessive amount of pills will cause damage to both parties it could lead to severe health issues,infertility, and even death.They have to mate and release phermones it's in their nature. So it's easier to let them choose their partners and provide birth control pills to prevent any incidents. However, every author is different.
I think in the prison, they prevent any pregnancy there, but to know that that blonde omega got pregnant because he spent the night with the alpha in the prison, really make me wonderr.. like why dont u give him condoms or pills to prevent it!