As powerful and knowledgeable as the Ascians may be, they are neither omniscient nor omnipotent.
Zodiark is the original primal, and tempering was apparently not something they were concerned with or a bug that had not been worked out. After being tempered themselves, the Ascians wouldn't be concerned with dealing with it, and in regards to their goals it's advantageous for mortals to be tempered (as primals are good for sowing chaos and weakening Hydaelyn).
One need look no further than dimensional travel to see their shortcomings; in over 12,000 years they did not figure out how to jump across the Rift to different shards while still in possession of a physical body, while Crystal Exarch G'raha and the post-8th Umbral Calamity Ironworks were able to do that in "just" a couple centuries.