Beowulf and Barbarossa
Secondary-neos referred to the Secondary monks of Hessra converted to neo-cymeks by the Titans.
When the Titans apprehended Hessra, they killed the Ivory Tower Cogitors (except Vidad). Their Secondaries attempted to defend themselves however they could not do much against the powerful war machine bodies. Involuntarily, they were converted to cymeks and for punishment, a set of torment-inducing needles, modified thoughtrodes inserted into the naked brain tissue.
When Quentin Butler made his coup and killed Juno, the Secondary-neos present in the surgical chamber did nothing to stop him. On the other hand, they helped him install his brain canister on Juno's body and start the attack against the Titans.
By that time, about 14 Secondary-neos were alive, and they assaulted the loyal neos to help Quentin and Vorian Atreides leave the planet.
When Dante, the last of the Titans was killed, the failsafe mechanism that kept the neos alive, was triggered and all neos on the planet died soon after.