Generic controllers can be used in any group endpoint and are meant to be used to further customized the integration to your requirements.
So you have the option to either setup a proxy item with the necessary rule triggers in-between your binding linked item and the skill to match the input value requirements, as @rpwong mentioned, or you can use the ModeController interface to set the mapping directly on the linked item. For the latter, just make sure to name the capability as “input”.
As a side note, a new metadata syntax for the skill will be released shortly. feel free to join the beta test.