And in fact I don't think he was ever referred to as an alien in the original Superman movies either (I think it was only ever alluded to with terms like "strange visitor").
In
Superman: The Movie, Supes spilled his whole origin story to Lois in her big interview, including the fact that he was from Krypton. That's how Lex Luthor was somehow able to deduce the existence of kryptonite and predict where to find a meteorite made of it merely by reading Lois's article.
In the Reeves TV series, Superman was pretty open about his origins; it didn't often come up, but at least the smarter villains, and several friendly mad scientists, knew about Krypton and kryptonite. I think I remember something about a scientist deducing what kind of planet Superman had to be from based on his powers. That might even have been the guy who synthesized the bar of synthetic kryptonite that was a recurring threat to Superman in the show.
On the radio series, which often had sloppy continuity, nobody at the
Daily Planet knew Superman's alien origin until Clark told them (narrating a rerun/re-enactment of the script of the series premiere), in order to convince them of the reality of kryptonite and the threat it posed. (Clark claimed that he'd gotten the story from Superman, and naturally the others didn't find that suspicious at all.) Even though Clark told them about Superman's weakness in strictest confidence, insisting it could mean the end of Superman if the public found out, Perry and Lois immediately betrayed him and spilled the whole story on the front page of the
Planet, leading directly to the theft of the kryptonite meteorite that only Superman and a few scientists had previously known about, which led in turn to the creation of the Atom Man, Superman's worst arch-enemy on radio, who came closer than anyone else to killing him. But I'm getting ahead of myself; a few weeks earlier in the storyline, when Clark was trying to convince Perry and Lois of the danger of the stolen kryptonite -- whose theft their betrayal and expose had been directly responsible for -- they didn't even recognize the concept of kryptonite and scoffed at the idea that anything could hurt Superman. Either the characters' guilt was so profound that they suffered partial amnesia, or the writers were so harried churning out new scripts by the day that they simply forgot what they'd previously established.
Anyway, there haven't been that many interpretations of Superman where his alien origins were unknown or a secret. There have been versions where Clark himself didn't find out until his adolescence or adulthood, but once he did find out, he usually wasn't that secretive about it where the rest of the world was concerned.