By looking at the figure on Wikipedia for the many-worlds interpretation of quantum mechanics, it seems like universes branch off as "observations" are made, where the outcome of the observation is one thing in one branch (e.g. cat dead), and another thing in the other branch (e.g. cat alive).
However, I think the many-worlds interpretation is more like: all possible universes always exist, with different amounts of probability, and these probabilities shift over time. And the way they shift depends on the distribution of probability, which seems to imply that the future of our current universe depends in part on the probability of various parallel universes.
This in turn implies that there isn't really one version of history, but rather, the current state of our universe feeds from a distribution of possibilities for our immediate past. I think this is what is meant by the statement in Wikipedia: "Many-worlds implies that all possible alternative histories ... are real".