I eMailed Pokémon.com this same question, and they said it was up to the interpretation of the fans. I'm not sure how to interpret it. Most Psychic-types are portrayed as intelligent (and many non-Psychic-type intelligent Pokémon generally learn a lot of Psychic-type moves, such as Noctowl), so that would point to them utilizing brain power. They also have a type advantage over Poison (mind over matter) and Fighting (brain over brawn), and a type disadvantage to types typically regarded as common fears such as the Bug and Dark-types, which once again would indicate the type's usage of their mind. However, Psychic-type trainers are shown levitating Pokéballs and doing various other unnatural feats that would obviously require the use of demonic assistance (just some examples being Psychic Sayid and Psychic Robert on Kalos route 10), so that could also mean that their Pokémon do the same. After hours of intensive and extensive research, I have yet to come to a conclusive decision regarding whether or not Psychic-types use their own brain, or receive demonic assistance. What do you think?
Please keep the subject on Pokémon. Also cite your sources of information if possible, but if not that's fine too.