I tend to think the concept of "Psychological" often is translated as zany, hyper, or hyperviolent, but I prefer to identify psychological stories as those that are primarily tied to being very very grounded and very rational in a setting that is hostile and closed.
Psychological could mean all sorts of tones, but the readers should feel claustrophobically in tune with the narrator/main character. That means no swapping perspective, a very close POV, so a reader can't be certain of anything but the MC, and the main character should be not certain of everything. The world should bottom out when the assumptions of the MC are revealed to be a lie, which should lead to the inciting incident or the falling action of the story.
The reader and the MC being in sync when things change, which lends it that psychological aspect. It feels personal, because the story *makes* it personal for the readers.
This means there can't be any dramatic irony until a second read/watch, because the turn carries the action. Many mysteries do this, because even when the audience knows the twist, the twist is powerful, just by the weight of change for the main character.
The story is not Psychological because it 'gets crazy', the story is Psychological, because the audience and point of view character are sharing the psychological reaction to the plot.