The thing with primals is that they seems to only be in Eorzea. Yugiri didn't know what primals were. The Garleans never encountered primals outside of Eorzea and they conquered most of the world. I believe theres 1 primal for each element. So if we include the elder primals then that makes 12.

12 and 13 seems to be symbolic in many SE games, especially this one.

I am more interested in Shivas beast tribe. Did the Ishgardians wipe them out? Or are they so few in number due the Ishgardians. It was said that she belongs to a never before seen beast tribe.