Of those, I'd only seen Millennium, which seems to have a strong tendency to revert to the "correct" timeline with the necessary action/reaction manifesting as a timequake. They never get around to explaining why the timequake doesn't affect all of the time between the manipulation and the time traveler's origin.
There's often an assumption of 'meta-time', in change-the-past scenarios like that. The 'reshuffle of causality' has to ripple-through the intervening time (though people
between the past-point and the future-point are rarely seen, to observe whether they 'feel' the ripple as it passes from one to the other). Or possibly its like a phased-array interference pattern, with minor oscillations being focussed upon the target (the point in the timeline responsible for causing the upset, i.e. in the vicinity of the contemporary time-machine 'gate') and only constructively interfering into a noticeable effect at that point.
Or imagine reversing the film of a droplet of water falling into a large body of liquid. Faint concentric ripples
converge on a point, providing just enough energy (in just the right way) to sloosh a droplet of water up and out of the now-still surface.
Whatever, it's usually tied to (and/or handily duplicated in) the scene-switching in the film itself, between past and future, the past-protagonist might be walking around the family home and the present-protagnist(s) are wandering around the old-and-abandoned family home picking up signs of things he did. (PastP hides something behind some books, PresentP (on a whim) looks behind the books and finds the item.) Not unique to time-travel plots, of course. The guy in the past can be 'native' to the time and the present-day people are reviewing prior events as a 'cold case', for some reason.
However meta-time can occur when (say) a vase is knocked over in the Past.
It wasn't knocked over in the present, but now it is, it can be seen. 'Time ripples' (i.e. minor versions of a time-quake) might happen. Present-day observers may or may not notice the effect (might depend on their real(meta)time link with the time-traveller), or notice that other (unlinked) people
aren't noticing, even though things like their clothes are changing, newspaper headlines are morphing and ruined buildings become rebuilt and built buildings become ruined, according to the consequence of the changes.
(A related literary example, Terry Pratchett's 'Mort', the titular character is 'out of reality' enough to notice that the 'wrong trouserleg of time' featuring someone's survival from assassination is being replaced by the 'right trouserleg' where she didn't. Whilst inside the Queen's Head tavern the 'interface' moves through it. Nothing much observably changes at first (slight clothing changes) but going out through the door he discovers that the tavern he is in is now called the Duke's Head. Nobody else notices (they are all living this other reality). They're far more disturbed that he went
through the door, but that's something else.
)
As a convenient convention, it is often taken that as realtime in the past passes for the person in the past (from the moment he arrives), similar realtime in the present passes (since he departed) before such changes to reality occur. Sometimes this is because the doorway-to-the-past is two way, and the time in the past you spend through the door is the same time that you are not present in the present, because you're through the door. Other times it's 'rule of plot', at best.
Whichever way, you could perhaps imagine it as a stack of parallel universe 'sheets', offset in the time dimension so that you travel 'n' universes over sideways (through the stack) in your time-jump and this takes you to the same-place-but-'m'-hours-earlier location in a partner universe, where m is proportional to n. In your own universe's past (by 'm' hours) the 'n'-in-the-future slice's time-traveller version of yourself might have arrived. Or maybe not, if (in line with your own actions, in the 'now' now, across whatever slices you travel) your actions in the n-sideways universe would in turn prevent the n-sideways, m-in-the-future version of yourself from travelling to the equivalent 2n-sideways point. (If this version is stopped, then the 2n-sideways 2m-in-the-future version of yourself will in turn still travel to the 3m-sideways 'verse, right. Just like you were able to do and -2n;-2m occured, stopping the -n;-m version that might have stopped your 0n;0m actions. Simple!) Whether or not the intervening layers in the 'stack' have their own array of actors/inactors doing similar things to interfere with each other at n±k equivalent positions throughout the stack.
I forget now how the rest of the series dealt with such paradox (I think it was more 12 Monkeys... more about that shortly), but the final episode of
Goodnight Sweetheart (man finds two-way temporal doorway back from 1990s London to the Blitz-era city) is bookended by the redecoration of a flat bought by the man for his WW2 use. When... something happens... he puts a message behind new wallpaper that he puts up, back in that time, just in time to be revealed by the contemporary redecorator of the '90s when he removes the very same 50-year-old wallpaper. If the redecoration had happened
prior to this point, would the message have been there?
Doctor Who's episode of 'blink' has something similar, driven by multiple instances of time-loops. The DVD messages existed before the person who ensured that they were there found themselves in the position of being able to start to prepare them, and the answers to the questions existed 'before' the questions themselves were asked (and enough details taken to allow the asked questions to
be responded to), but then we've already touched Doctor Who's... flexibility... with such things. As an example, in a pre-restart series... 3rd or 4th Doctor..? ...there was a case where Doctor and companion are dealing with a pre-'now' invasion of Earth and the companion states that
obviously the invasion failed, because they know Earth is unscathed... one quick (surprisingly consistent and unmisdirected) trip back to the present in the Tardis and the doctor shows the 'ruined now' of Earth, that
will happen to the past they have just left, and so they return to the past (again, the Tardis's steering seems surprisingly glitch-free) to thwart the invasion and create the 'non-ruined now' again. (Yes, probably absorbed by the same thing that the Master tapped into his captive-Tardis paradox-device to allow the Tochlafane to subjugate Humanity, despite the eventual problems involved in
that being possible... which, as it turns out, doesn't turn out...)
Anyway, as you apparently haven't seen it, my reference to 12 Monkeys is regarding its stable time-loop (assuming you don't explain it away as something
entirely different). As a young boy, the protagonist witnesses something. Limited information about the 12 Monkeys comes from some time between the present and the future. In the future, the protagonist is tasked to find out what actually happened via time-travel. Back in the past, he features (has already featured) in the event he witnessed as the young boy and is instrumental in the generation of the original information about the 12 Monkeys. To say much more would be a spoiler beyond the level I'm prepared to go.
Personally, I like the 12 Monkeys plot (done well, you don't even need to be fooled into thinking it won't be one, because there's still things to discover!), insofar as it fits my world-view of how time-loops work. However, I'm equally happy with (good) flip-flopping timeline plots, branch-generation plots, etc, if they measure their resilience and consistency well to how hard/soft their intrinsic 'background science' is.
Thus, Bill And Ted's Bogus Journey ("...we just need to remember to come back and put the key where we can find it... ah, here it is...") is a good treatment of 'soft' time-loops, if a bit deus-ex, but also Interstellar... (in ways I won't describe, because it's maybe still on some people's to-watch lists).
The
classic (original?) Time Travel/Butterfly Effect story "A Sound of Thunder" by Ray Bradbury works for time-branching/redoing, exactly enough for the setting, and then of course HG Wells's own "The Time Machine" appears to avoid such problems by the sheer scale of time, ditto A Connecticut Yankee in King Arthur's Court (in most variations). There's a short story equivalent (which I wouldn't nowknow the name of, or how to find) which has a female 'merlin' from the future looking for a 'likely lad' to create a myth around with her own technologically-inspired 'sword in a stone' (anvil) setup (a tidally-powered waterwheel sending crude electricity through crude wires into a crude electromagnet which is the crude mechanism behind preventing anyone 'unworthy' from drawing the sword... unless she cuts the power, for the person she selects), and that hints at the same bootstrapping mechanism as the "...and how do we know
he isn't the inventor of transparent aluminum?" part of Star Trek IV: The Voyage Home.
The Narnia series handles time-differences by (as well as a degree of overseeing omniscience/omnipotence by Aslan, no doubt) having separate worlds, anyway, with conveniently differing flows of time, and, besides, it's
magic and mystical!