When you tag host elements, you can sometimes edit the value that displays in the tag, thereby changing the properties of the element. When you tag linked elements, however, you cannot edit the tag to change the properties of the linked element.
When tagging rooms from a linked model, if a room in the current model overlaps a room in the linked model where you click to place the tag, then the room in the current model is tagged. This behavior is consistent when tagging areas or spaces. When tagging other elements from linked files that may be overlapped by elements in the current file, press Tab to highlight the element in the linked file to make it accessible for tagging.