I have encountered true stage managers in the symphonic world only very rarely. More often, there is a staff member who is either called the Production Manager or Company Manager, and they handle setup, riders, tech schedules, house needs, etc. After loading into a house, the house SM (who is IATSE) is given a cue sheet - along with all riders and schedules, etc - and they call the show. Or this orchestra staff person calls the show themselves. Usually they're only calling curtain/lights up and then 2 hours later, curtain in/lights down.
Whether your musicians are union will be extremely important to set the parameters of how you work with them. Often with an AFM orchestra, one of the orchestra members is the official attendance taker and schedule creator for the musicians. This person is also union, and must be by contract. If a musician is late, they are docked pay - also by contract. But the musicians and the union require that this is all handled exclusively by union members. So in my experience, this means that you are handed the schedule from this musician union schedule person (and it's always accurate, correct, and acceptable - again, in my experience), and if a musician is late, you - the SM - are absolutely not allowed to call them. The union schedule person does this. Oh, and your SM watch gets synched to the union schedule person's watch so you both agree on downbeat time, etc.
But if you are working with a small chamber ensemble, it sounds unlikely that they are union (yet). And they probably need someone to handle venue issues and bring the lights up at the beginning of the show. It's great that they want to raise the bar of professionalism by making this position union. I think IATSE might apply the best in this situation.
