When you look at what limited information that surrounded the calamity they faced the highest possibility of why it happened was because of their creation magic. If you look at the people themselves they did everything they could to avoid confrontation and bottled up their emotions. So when something happened that started the calamity in a far off city state it caused fear to become widespread, as the calamity spread that fear manifested more monsters to propagate it further which lead to even more cases of the Ancients becoming overwhelmed by fear and summoning forth more monsters. After all, all it took for them to use their creation magic was a mere thought and all it took to produce a different result was another thought.
So what would be one way to try to prevent this from happening again after the laws of the world was repaired from the rampant unrestricted use of creation magic? Tempering. If Zodiark tempered everyone and controlled their emotions then even if something were to go wrong and monsters get summoned no one would fear the monsters and lose control of their magic because they cannot feel fear unless Zodiark allows it.
So of course Zodiark naturally tempered them. It was part of Zodiark's design to begin with as an anti-terminus measure.
Hydaelyn though is the antithesis to Zodiark. She was summoned by those who did not agree with the sacrificing of unwilling life and those who did not want to be controlled like puppets by a creation of their people. So they summoned Hydaelyn to be a check on Zodiark and to ensure that the life that was restored had a chance to have a future of their own. As well as sunder the creation magic of their people so that the calamity could not come to pass again while still allowing everyone free will. Which every action of Hydaelyn checks out in regards to that. Not to mention our ability to question Hydaelyn is proof of us not being tempered. Just as the Ascians inability to question their god or truly consider alternatives proof of them being tempered. Hydaelyn wants us to make our own future, to live our own lives. Zordiark exists to control lives and maintain a state in the past.
Every other primal that does tempering works off of ascian blueprints, and those primals were purposely designed to be as destructive on hydaelyn as possible.