Shooting indoors for green screen with the Sony HDR-CX560V manuel or auto settings

Greetings,

I have the Sony HDR-CX560V video camera and am trying to shoot a dark "Chubacarba" puppet indoors with a green screen behind it.

I have many lights on the subject and am using back-lighting for the green screen. No matter how much light i shine on the puppet it still looks kind of dark. The green screen is working though. Is it the auto settings that are adjusting to the lighting, would it be better to go into manual settings to shoot a subject indoors or that won't make the subject looks so dark. I know these cameras are good in low light so what is the problem? Is there a preset for the kind of settings that i need? I know it's in the Manuel but perhaps green screen shooting is different.

Thanks for your help.