Many, many, many time travel systems are based on branching a new timeline off from your universe and creating a new one that starts from the past. If you want to go back in time, that's a new timeline; going into the future lets you stay on the same timeline. In general, you can't change YOUR past, but you can tweak something at T minus 100 years in a new timeline, and then see the effects of that in the future of that timeline.
Fun corollary of that: Under this system there would be one 'original' timeline. Anyone who goes back into the past from this timeline simply vanishes, with no evidence that going backwards is possible at all.
I'm -pretty- sure this is the system that the Terminator series uses, but maybe not. If the world is totally hosed in 2100 AD or whatever, you can't save it, it's gone. But you CAN try your damnedest to create a new universe in which the world isn't hosed. I'm not sure why the robots would be so insistent to kill John Connor if they already won the war in at least one universe, unless they want to spawn a universe in which they win it -harder-...
Although I guess when you jump to a new timeline spawned from the past, you probably can't go back to your old timeline, and there's no way to tell if it even still exists. So meh, maybe there's only one active timeline at once and everything else gets pruned.
The main important points are that with this system, time travellers are not affected by changing their own past...because they're not. They are inserting themselves into a new timeline at an arbitrary point, which happens to have 't' be earlier than the 't' in the timeline they left.
This has nothing to do with Achron
But it works fine in sci-fi in general. Paradoxes are fine. The only things that piss me off are time LOOPS, like where you turn out to be your own dad or something. You can perpetuate a cycle through time travel, yes, but you can't have information be its own source...
...Right now I'm trying to figure out what's going to happen on a major TV show I like, which the creators previously claimed wouldn't have time travel, but now has some seriously blatant time travel with scary world-breaking things happening in it.
LOST. Someone who's alive in the present just died in the past. Just how time travel WORKS hasn't been gone into in very much depth. So for all we know, the next episode could start with the world exploding, or the present-day person dissolving into vapor, or with nothing happening at all and someone saying 'Yeah it doesn't work that way'. Me I'm hoping for explosions...