Except that's not how Astral and Umbral aspects work. When the Lore Book gives an example of what the difference between Astral and Umbral are, it uses the same element, fire.

Quote Originally Posted by Encyclopedia Eorzea
In addition to the six elements, there also exist two poles -- astral and umbral -- which greatly influence the nature of the elements -- an astral charge bringing more activity, while an umbral charge resulting in more passiveness. For example, when in an astral state, fire exhibits high volatility, whereas its umbral state is characterized by dryness.
All six elements can be astral or umbral. You can have Astral Ice just as you can have Umbral Fire. In fact, two of the weather patterns in Heavensward are Umbral Static (in the Churning Mists) and Umbral Wind (in the Sea of Clouds).

As far as I can tell, Astral and Umbral have nothing to do with how the elements relate to each other. That relation seems to be something intrinsic to the elements themselves and no mention is made of the aspect the elements have.