Carrie sees her understudies as lesser and not on her level. For her, it's like if your boss sat in your office watching you work all day. Some people would get intimidated by that. She thinks she is "better" therefore, in her mind, her understudy would be intimidated if they knew she was in the crowd watching them/judging them.
I'm not sure if I'm explaining this well, but I think that's the way she thinks about it all. "If I was the understudy, I would feel intimidated if the principle actor was watching me."
I don't know how popular that thinking is, because others see understudies as no lesser than the principle actor, therefore there is no levels to it/they see each other on the same level. Like I've seen the principle actor make a congrats excited post about the understudy many times.
I think she also gets possessive about her roles too. kinda like "Why watch them, they won't be as good as me?" Or she is too frightened to watch them, incase she watches and feels like they are better than she is. I think someone doing "her" role better would send her on an insecure spiral.