Absent details of a specific implementation, "the very concept itself" is just a vague one of "mysterious powers of the mind".
In OD&D and AD&D, that covers more than purely psychic phenomena. Teleportation, for instance, is thoroughly physical.
The association was a byproduct of the trend to dress up magic in atheistic drag that was superficially more plausible to the modern mind. That is still big business in the world beyond honest fantasy fiction. In the 1970s, not only was there another boom in interest in allegedly real "psychic powers" (along with resurgent spiritualism), but popular fiction and film -- such as Carrie and Escape to Witch Mountain -- capitalized on the fascination.
Adventure novel series such as Andre Norton's "Witch World" and Marion Zimmer Bradley's "Darkover" were also hits. If memory serves, both (along with Moorcock's "Elric" and much else) got filed under "science fiction" in the 1960s-70s, the "fantasy" section not really burgeoning until the 1980s.
The term 'psionics', I think, had attained even wider currency than formerly via comicbooks and television in the 1960s. Rules for powers so termed appeared both in D&D Supplement III (1976) and in Traveller Book 3 (1977).