The changes in color are to do with your camera. You need to "lock off" the exposure and white balance. Most cameras automatically change the color and brightness when the subject matter changes,(when you move your hand up to the lens and watch the brightness change) to keep an even exposure. The problem is in animation this becomes flicker as the camera shifts between frames as you move your puppet or subject.

Video cameras:
Try the camera menus to see if you can lock the exposure and set the white balance to tungsten or whatever your main light source is.

When you start a new project in SMP, and the capture settings window comes up, select your webcam from the drop down, then click the "Format" button.  this is where you can change a lot of these parameters.  Take them off default settings (you can often zoom and pan as well) and click apply to update the live view.

Try to avoid sunlight or exterior ambient light because this changes a lot.  Reflected light from yourself or clothes can also effect the color/brightness.