Each Member faced a crime committed by one of his "brain images". They Committed crimes for Brainwave (even carrying away loot) and killed. People shot would die only to have even the bullet wholes disappear from their body and all signs being death by shock and fear. Images that could physically fight Spectre, sandman, Hawkman etc. That could bind Wonder Woman, even carry the adopted daughter of Johnny Thunder.
It was retconned later ( All Star Squadron) that his first encounter with the JSA was a year or so earlier. That he encountered them earlier and had placed a mental command telepathically into their minds. Even so far as to telepathically push the Spectre to seek out some other danger (believing him to be the only one of the JSAers he was not yet powerful enough to face.