My speculation's based on previous full moons, as the population here would act strangely on the week beforehand. Impulsive gambling being one of the earliest cases. At first, I thought it's because they have strong powers, but their connection to the human mind might be related.

Mr Garviel seems like a soldier and Saber seems like she's from of high standing. They would sometime call for a group meeting at Saber's workplace so we can compare information and our abilities to cover our weaknesses.