In each sect, there were actually some individuals from other sects implanted within. They couldn't be called spies, but sometimes they were the first to know when something happened.
In the hearts of each sect, they also knew who these people from other sects were, an unspoken understanding because everyone did the same.
So when the news of Chen Fei's breakthrough to the Aperture Tempering realm spread among the inner disciples, naturally, people from other sects gradually became aware of it too.
The birth of the Aperture Tempering realm was a big event for any sect. Even dominant forces like the Immortal Cloud Sword Sect attached great importance when a Aperture Tempering realm cultivator appeared among their disciples.
The Primordial Sword Sect was no exception, let alone Chen Fei's breakthrough, which took just a little over a year from becoming a true disciple to that moment.