Astaroth had seen the message about infiltrators in the guild chat, but seeing no response from Phoenix to it, he assumed she was already taking care of it. He trusted her completely to prevail, no matter the number of enemies she would face.
Many people thought him or Khalor to be the most formidable player in Paragons, but he disagreed. Admittedly, they were the strongest, in terms of raw combat ability, but he didn't judge power off of just those scales.
To him, players like Phoenix, or Athena, that had high adaptability in any type of situation were much more dangerous. Athena had already proved she could be resourceful in the past, and he knew she would many times in the future as well.
As for Phoenix, he was well aware of her tactical mind and strategic thinking. Many times, in war, leaders would be rigid about their strategies, and stick to what had been pre-planned.