you are trying to select refinement regions on a finished mesh. This is not yet supported. Therefore the assignment box does not allow you to add entities.
In order to assign the refinement faces you need to delete the result of the mesh operation first and then select the faces on the geometry again. If you want to keep your current coarse mesh you can simply duplicate the operation. The screenshots below show how to proceed from your current status:
The UX of this work flow is right now not on the level that we want to provide. We are investing to make the assignment simply also work on the finished mesh. Until that point you need to unfortunately stick to the proposed work around. Please not though that this is not related to the new assignment workflow. Mesh refinements were not possible on the finished mesh result in the past as well.
Hope that helps!