Funnily enough just read about causal loops as part of a deterministic view on time travel just before reading that last post.
Oh, the Demon with a Glass Hand story pattern.
I wouldn’t assume that Outer Limits episode was the first example - John seems to have found an older one, and I suspect that Jack Williamson’s The Legion of Time would also fit - but if you’re talking about the media treatments of the theme, it always seems to get mentioned in the footnotes.
But really, I think that trying to find a label for it is excessively fine sub-genre categorisation. Once you have time travel as a working sub-genre (thank you, HGW), this is one of the fairly obvious forms that a time travel story can take. And it has distinctly fuzzy edges. Does it have to be limited to a present-day setting, or do you allow, say, The Guns of the South in? What about people starting in the present, but ultimately jumping all around time, as in, oh, The Corridors of Time? How hard do the future-people have to try to change things, and how much ironic failure do you allow? If your usual setting is the future, but the cast sometimes jumps back to our present and then tries not to change things, as in a couple of Star Trek episodes, does that count?
Anyhow, if you must have sub-sub-genre labels (and I think this may even be a sub-sub-sub-genre), I rather like Days of Future Past, mostly because I think both the comics and the movie versions were quite good.