Use a hue/saturation node to shift the hue, and then remix that with the original image using a mixrgb node, the mix factor being the mask image. Looks like this:

Use a hue/saturation node to shift the hue, and then remix that with the original image using a mixrgb node, the mix factor being the mask image. Looks like this: (Color mode for the mask actually should be 'Non-color')