I haven’t read the book but the best answer would be A. Reason is that August is being nice to her and she can trust her.
When added to the word detect, the suffix which means "a person who" is -ive.
"A person who" means that you need to create a noun which refers to a person by adding that suffix. If you add -ive to detect, you will get the noun detective, which is obviously a person.
The word detectary doesn't exist, and the word detection doesn't refer to a person, but rather the act of detecting.