We don't know how efficient his power is. We don't know much about that power actually.
The lies the girls said were more a way to motivate themselves.
As for center girl, it might be she's got a power too with one of the effects being to disable Manager-kun's.
But truth is my cynical mind just remembered politicians are fairly good at deceiving lie detectors

As for manager-kun, he might not be a jerk, but it certainly affects his life an interactions with people.