It looks like everything is working as it should - note how that particular present is making the curved edges and bevens shine. It's also having an effect on the front faces of your object - but in a more subtle way. If you watched a rendered animation, you would see how the different parts of the reflection map affect the front surfaces.
A chrome look is best accomplished by using a black base color and a black and white reflection map with the reflectivity cranked up.
A couple of tips:
It's not necessarily a good thing to use the same reflection map for edges and faces. experiment!
Make your own reflection map out of colors in your scene - it will help the animated 3D elements appear to be part of the scene.