An imaginary tale is just a 'what if' tale outside of regular continuity. And Ultraman and the Crime Syndicate were on Earth-3..the original superheroes were on Earth-2.
But the problem with this line of logic is there really was not a "regular" continuity and writers basicly ignored the mass they had made of things until Flash of Two worlds (1961) showed up and gave a really nice out - alternate Earths. Then the flood gate opened and Earth-2, Earth-E, and Earth-B were put forth in the 1970's to address all the major continuity glitches that DC had allowed.
Trying to pin down if you are reading an Earth-2, Earth-E, Earth-1 or Earth-B story is about as fun as trying to figure out Hawkman's Post-Crisis to Pre-Zero Hour history. As far as Superman is concerned Earth-2 he works for the Daily Star, Luthor has a full head of hair and he has another archfoe called the Ultrahuminite. Earth-E he lives in the same time period as the Superman of Earth-2 but works for the Daily Planet and Luthor is bald. Of the the two only Earth-E was a Superboy but he was kept busy at home by Luthor, some take over the world aliens, and 5th collunmists)
The Earth-1 Superman is the one everyone is most familar with: he was Superboy, knew Luthor as a kid, never had a foe called the Ultrahuminite works for Daily Planet and so on.