The word you're looking for is continuity, and it's what I have a problem with here. Not that FF7 has had flawless continuity, but at exactly what point in time within the FF7 continuity did Cloud and Sephiroth get whisked off to some other world in which all the other FF heroes and villains also exist?
Whenever Chaos decided, "Fuck this shit, I'm returning everything to discord and shattering FFVII's world and taking Sephiroth out of it to fight for me" and Cosmos decided, "Well shit, if he's gonna take Sephiroth, I might as well get Cloud!"
Time and space do not matter to gods. They fashion reality and existence. There is no exact point in time in FFVII's timeline that it happened because in Dissidia, FFVII's entire universe was annihilate and consumed by discord. All that remained of its existence was the Planet's Core. All we know is that it was at some point after FFVII, and before AC.
Did they get placed back immediately into the FF7 timeline at the same moment at which they left—as in the Back to the Future analogy that someone else mentioned—with no memory whatsoever of the events that took place within Dissidia? Only under these circumstances can I find myself accepting Dissidia as part of the FF7 continuity, and in that case it wouldn't even matter what happened in Dissidia because it had no effect on the behavior of Cloud or Sephiroth afterward.
That's exactly what happened. That's what Dissidia's storyline and ending is all about. When Chaos dies, the discord is gone, and everything is reverted back to normal, hence the crystals return each character back to the world. What they remember or not is up to interpretation.
And I have to judge the decision to attempt to include AU—it has to have taken place in an "alternate universe" in the literal sense even if Cloud and Sephiroth were taken to an alternate universe within the FF7 continuity, because the other FF characters and worlds don't exist in the same universe as one another, with exceptions like FF7/12—as an actual plot device as nothing less than stupid.
Each Final Fantasy takes place in separate universe and dimension. However, each world of Final Fantasy is connected by the Interdimensional Rift from FFV. That's the tunnel that connects them. Yeah, Dissidia is an "alternate universe" from FFVII's universe. But the characters are from their own, originating worlds and dimensions. There's nothing stating that these are anything but the true-blue FF characters. Kitase even stated that he didn't want this title to be considered a gaiden or spin-off at all, for Christ's sake. He's literally saying its as official and true as it gets.