Dave, Knight of Time, able to travel between two different timelines and not just up and down his own. This isn't even normal time travel where one goes up and down, this is sideways stuff.
I don't think Dave is traveling "sideways" into alt. timelines. Trollian's viewer is inaccurate, because the timeline isn't a series of parallel lines - it's more like a tree of all possible outcomes. Thus, doomed Daves aren't exactly hopping to another branch or twig of the tree, they're moving 'down' the tree and backwards into the past, where their actions prevent the doomed timeline from even existing in the first place (see: Davesprite). The timeline from which they came not existing anymore retroactively dooms them too, because they have no point of origin for all their memories of the doomed timeline.
Terezi's case here is special, because it's not immediately clear who is the doomed and who is the alpha. Both Green and Redshirt Dave in this case traveled back to what we definitely know is the alpha timeline, but since they both traveled back, one is doomed, while the other isn't. At this point, we can't tell which one is doomed (although I think it's redshirt Dave). Terezi is smarter than she looks, because she gave pre-flip Dave the instructions for both outcomes, meaning that the doomed Dave wouldn't need to communicate with her (which he couldn't because that was a doomed timeline) and thus reveal which Dave is the doomed one. As to why I think Green Dave is the doomed one, it's because Redshirt Dave has waited a day, and possibly communicated with Terezi telling him to go back and kill himself. The communication means that Redshirt Dave is definitely in the alpha, as Trollian can't talk to doomed timelines.
Finally, there's the point that the timeline appears to split fourways, because of the two possibilities of the flip and Dave's two choices. What if Terezi hadn't actually flipped a coin, and instead told Dave that it came up bad heads? That would mean the timeline only split twice.