It’s like hypnosis. If you do weird shit in a dream, that has nothing to do with reality, it’s not going to matter when you wake up. But if something happens in the dream that affects a core emotional belief, it could affect you when you wake up.
Say, you’ve been feuding with your sister over some silly fight, but in your dream you remember some day you spent together as kids when you really felt her pure sisterly love. When you wake up you might realize the silly fight has been obscuring your deeper. bond and decide to reach out.
In the same way, all the running around chasing and shooting and intrigue stuff will fade when he wakes. But his core emotional belief that his father was disappointed he wasn’t more like him has changed, and he now views his father differently, and believes he probably wanted him to forge his own path.
Not because they convinced him - they specifically said that doesn’t work. It’s because they manipulated him into coming up with the idea himself and believing it was his own. Because of that factor, he still believes it when he wakes up.
Also note that unlike your pentagon example, it relies on using memories or experiences that were originally ambiguous and not contradicting of reality and therefore open to reinterpretation.