The cult of Tesla was conceived of, and initiated by,...Tesla!
Tesla courted the press and gave many, many interviews over the course of his life. He developed a way of speaking about himself and his inventions that subtly incited the reader to be amazed by his thinking processes. He was not unlike Houdini in that regard. Just as Houdini created his own legend, the legend of Tesla was created by Tesla, and so was the notion that he was under-rated compared to Edison. No one disseminated that latter idea more than Tesla did. Like Houdini, Tesla had a long period during which he gave lecture/demonstrations of the fantastic effects he could produce with high frequency-high voltage electricity. Shooting long sparks out of his fingertips and causing evacuated tubes to glow in strange, colorful ways, gave him the aura of a kind of electrical wizard. First and foremost, Tesla was a showman.
To his credit, though, he knew he was a mere EE and inventor. I'm not aware he ever tried to pass himself off as a physicist or even a scientist.