Hey ,
Promotions' condition mechanism checks if group/customer/cart fulfils requirements. If it does, it fires action.
Visibility is not involved in this mechanism.
You can switch in BackOffice in promotion rule view in section Rule Properties whether promotion is visible or not in storefront view. But it will affect every user.
If the promotion is working as you described, it works as dev team meant it to work.
To answer your question fully, I need to add that "visibility for promotion-dedicated-for group" might be achieved. It would require some investigation and further custom development. In this case I suggest you to contact Expert Services.
Best regards,
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