The Meteia are entelechies. They don't directly create despair themselves. They take the emotion that they encounter in others, amplify it, and give it form. You'll remember, for example, that Meteion enjoys candied apples, even though she cannot eat, because of the emotion she feels from Hermes when he does. If joy was the predominant ambient emotion that the Meteia had encountered on their travels, then we'd be fighting off sunshine and rainbows.

We know for a fact based on the in-game text that the Amaurotians can neither manipulate nor be manipulated by dynamis due to their aetheric density. If it was that easy, then they would have simply killed themselves like many of the other civilizations that the Meteia encountered. Their underlying emotions can still be perceived by entelechies, however. We know this from the Elpis bloom phenomenon. The Amaurotians' despair was their own, not Meteion's.

We also know that there always needs to be an initiating event to get the ball rolling. In Thavnair, Khalzahl's business fell on hard times and he lost a critical trade deal, causing him to go into abject despair. It's only after he transformed that the sky began to burn. Likewise, there would have needed to be an initiating event in Amaurotian society, where someone's despair got the best of them, leading to the creation of the first terminus beasts.

The Amaurotians themselves tell you that it's quite common to accidentally give form to an altered concept based off of the workings of your unconscious mind. In some cases, this leads to a fortuitous discovery. With Meteion's influence, however, none of that was safe. Nor, I suspect, were any of their existing creations, while we're at it. Perhaps even moreso given that Lahabrea's group were experimenting with merging souls with creation magic at precisely the wrong time. Who knows what happens if a less aetherically dense construct fused with an Amaurotian soul, like a hemitheos, catches the dynamis flu. I wouldn't be surprised if the raid series elaborates on this further.