I've worked with dogs, rats and pigeons onstage, and you definitely need to have a "meet the animal" meeting with the performers, including full instructions on how to behave around the animal, what the animal can do, how to deal with the animal if it misbehaves, and what can be done to attract the animal. Let the animal smell the whole cast, and be slowly introduced to everyone. If it responds to certain treats, have folks stationed on either side of the stage with said treats in case of distraction. Pigeons will go to the brightest light when in a dark environment, so that's how we cued it to land in a specific spot. Is there something like that that will attract the monkey if it gets off leash?
I'm hoping that the person working with the monkey will have it leashed, and you should have someone assigned backstage to be its handler - even if its not the actual handler. I can't believe that the handler is being that non-chalant about leaving their animal with a theatrical troupe. Has the monkey ever been onstage before? With lights, sounds, and live audiences making noises? I would have one, preferably two, folks who's job backstage is solely the monkey.
-Centaura