In the setting of this question, magic exists. Psionics also exist, but only in a sub-sect of the world's population, in a sort of cult.
This instance of psionics requires no components, verbal or otherwise, beyond thought, though their abilities are limited in range to what they can see. They can duplicate any effect that magic can, but must be mastered through practice to simulate higher level magics, so inherently they are no more or less powerful than other wizards/sorcerers of equal practice/innate skill.
The cult keeps psionics as a whole, completely secret, but does not limit its use in any way. Those with the ability are no more inherently good or evil than any other person.
Because psionics are kept secret, assume there is no magical way yet developed to detect it, as the wizards/mages/etc have no idea what they would be looking to detect.
The question: Barring one of the psionics explaining the secret, how might it be proved that the results of psionic activity are not the results of typical magical activity?