There are 2 ways around this problem.

One easier than the other:

1. You can do an animated alpha by hand in Fusion.

or (easier)

2. You could duplicate your scene, and rename it so you don't overwrite the original.
Then you can apply the "Use Background" shader to everything BUT your box.

That way, you will get object "occlusion", meaning it should comp normally like in your first pic.

Does that help?