It's a challenge; as with a lot of D&D class concepts, it's often easier to define them by exclusion (this character is not a "Class X") than by specifically required traits. (See: ranger).
If it uses a bunch of highly visible effects, especially elemental effects, probably not psionic. (Although see: Carrie, and the Emperor's Force Lightning) If it has strong medieval trappings, probably not psionic. If their abilities use some sort of ritual or spoken word triggers, almost certainly not psionic. If it heavily codes towards another well-known fantasy archetype (see: Gandalf), also not psionic.
Likewise, if their ability set is strongly defined by telepathy and telekinesis, it's likely a psionic-type character. If the manifestation requirement seems primarily mental/emotional, it's likely psionic. If it has more modern-day or science-fantasy trappings, it's more likely psionic.