Pre-compose your footage treatment, then mask. AE has such a thing as a render order, you know...
i just tried that but the mask still doesn't work. The mask doesn't cut off any of the footage.
You probably did not move all attributes to the new comp.
You could also use a track matte.
Really doesn't address the real issue. I understand and have read the render order documentation and still run into this issue at random. Precompsed layers which I then apply the shift channel effect to will still randomly ignore their own masks inside the precomp. To be clear, it only happens about half the time, it isn't happening to a layer with both the masks and the effects in the same comp, and it is incredibly frustrating how random it seems.
My current workaround is to precompose the layer that needs the effect again before applying the effect, which just adds unnecessary layers of obfuscation.
TL;DR precomp again if you still have the issue, but you shouldn't have to, the render order logic should only need as single precomp.
please provide screenshots so we could examine your workflow exactly in relation to what you are trying to accomplish, and if you can - a project file that illustrates your problem.