How did the vets that were in the operation balance it if they were killing the monkeys?

This is similar to your other question. The vets basically had to balance the greater good with the harming of animals. The potential cost of a deadly airborne virus to human populations would be devastating.

The veterinarian's oath is a code of honor that bounds all veterinarians to take care of the animals as well as the saving of human lives through medicine. The vets had to keep their emotions to one side and try to find a balance between both humans and animals, some told themselves that finding a cure for Ebola was research that could help save human lives and possibly avert a tragedy for the human species.