Atoz tries to push Kirk into the portal and send him to another time. However, as established earlier if a time traveller isn't prepared then they'll die. It's also established that if a time traveller is prepared for a historical era, they can't survive in the present. Since Atoz is trying to save Kirk's life, he must have used the Atavachron to "prepare" the captain for whatever era he's sending him too. But... there's no indication and no time available where Atoz can or does unprepare the captain so he can survive in the present.