How do I add a tab detached from an entity's domain?

To build a custom tab you will need to tap into the AdminBasicEntityController.modifyEntityForm(...) method.

In this method, you can add a new tab and even provide a custom html template which can then hold all the elements needed for your custom logic which can be set in a custom admin controller or in the extended product/customer admin controller. Here's an example of how we do this (from the OMS module):

protected void createOrderTab(EntityForm ef, Order order, Integer tabOrder, String tabKey, String component) {
        Field field = new Field();
        field.getAttributes().put("order", order);

        FieldGroup group = new FieldGroup()

        Tab tab = new Tab().withKey(tabKey)
                .withTabClass(" oms-tab oms-order")

Note that depending on the entity you are working with, you may need to override a more specific admin controller such as the AdminProductController or AdminOmsCustomerController