It is unknown if Tinker was exposed to the ALZ-113.
Tinker never appeared in Dawn of the Planet of the Apes. It is possible that Tinker had died before the events of Dawn, or simply wasn't seen on-screen.
It is also unknown if she and Rocket have other children.
There is a fan theory which speculates that one of the female apes looking after Cornelia when Caesar returned from the dam to find her collapsed and ill may have been Tinker; specifically, the female crouching over her that wasn't wearing a "mask" bears physical resemblances to Ash. This is not confirmed.