According to common sense, there should be a substantial "verification period" between the arrest of a suspect and the conviction.
The Immortal Sect is a place that values reasoning; one can't convict someone without evidence, right?
But the "Capital Exorcism" case was different because the captured Demonic Tao cultivators weren't fleeing to a factory for refuge; they brought their treasures (evidence) with them.
Such things as Demon Sect disciple rosters, meritorious service records, sect meeting minutes...
Including various unaccounted for Spirit Stones, Magical Treasures, and Elixirs...
And of course, illicit Cultivation Techniques, Formations, and Talismans...
Naturally, the most explosive find was that many Demon Sect disciples liked to keep diaries.
They say normal people don't keep diaries, so the abnormal ones have to.