I think it's speculating with your own "vain imagination" to assume that he's using only his imagination. He's an experienced exorcist. That means he has more than just imagination to go on.
And why would you limit yourself to the words of Scripture? Demons are real, therefore our experience of them is real, therefore it stands to reason that there is evidence for them that comes from our own experience, and from the application of the wisdom of holy men, in addition to that found in Scripture.
Scripture has nothing to say about the hazards of being a careless pedestrian in automobile traffic. Nevertheless, I think you're probably aware of those hazards and take steps to mitigate them in your own life. Why? Because you have actual, lived, experience of those hazards. Exorcists have actual, lived, experience of demons and their behavior patterns.
Very well put!