Just to quickly clarify, I did not mean to imply that Zodiark and Hydaelyn are anything more than immensely powerful aetherial constructs. They were created by more sophisticated and controlled methods than our new primals, thus its possible that there are some rules or flaws (that stem from the improper method of creation used today) that don't apply to them. I think Emet just found it tiresome to explain such differences on the spot, thus used the blanket term "primal".
As for the tempering part, I think its still a possibility that the WoL is tempered. We are just now starting to scratch the surface of what tempering is in the story. We know very little, and even less about what being tempered by one such as Zodiark would mean.
There is a theory floating around about Zodiark and Hydaelyn representing control vs freedom, and that somehow manifesting in their form of tempering. I find this to be probable, but I would prefer if they didn't take this road.