FYI: Both interpretations are equally fanciful and unscientific. You can't go back in time just by going real fast.
Unless you're slingshot-ing round the sun, of course!
Well, that's actually borderline plausible, since it's not just speed, it's dealing with the spatial distortion of gravity wells. The original "slingshot effect" in Star Trek was around a "black star" (the term "black hole" was still a year away from being coined at that point), and about seven years later, physicist Frank Tipler calculated that you actually could theoretically travel back in time by traveling through the distorted spacetime around a supermassive rotating body such as a black hole. As for slingshots around the Sun seen later (in the same episode and elsewhere), those involve a starship's warp drive, and any FTL drive is potentially a time machine according to relativity.
But it's a cartoony misunderstanding of that to assume that if you just accelerate fast enough, you can exceed the speed of light and thereby go back in time. You can't get above lightspeed just by hitting the afterburners, and the time travel/"causality violation" issues in FTL travel have more to do with events after you exceed lightspeed than with going back into your own previous history. And that's leaving aside the more basic absurdity of someone with the shape and appearance of a human being having the ability to fly or accelerate without any evident form of thrust. The whole premise of Superman is pure fantasy from the start, so arguing that "he flew real fast and went back in time" is somehow more plausible than "he spun the Earth backward and made time reverse" is taking hairsplitting to a superhuman level.