you need to have a skeleton, a model and the model needs to be skinned to the skeleton,
fbx wont take into account the controls you created so there is no use for them after export.
just create an animation with the controls and bake this out onto the skeleton (edit>keys>bake ...)
get rid of the controls so you keep the 3 basics
test if the animation still works and look if all the joints in the skeleton are keyed
then you can export all from maya to an fbx file and make sure that animation is checked
geometry cache will not work in fbx or at least i have never tried it as it is easier and cheaper to export skinned meshes instead of vertex animation, and this way you will be able to edit the skinning and the animation in 3ds max afterwards