Worlds apart - Multiverse
In those theories both worlds start equal. They are perfect copies of each other. When a time traveler from the future visits the past he will enter the parallel world and from there on the two worlds start being different. The future of the world that the traveler visits changes and moves in its own new direction. Not only a time traveler can cause these changes but also a simple message from the future could do that. In this respect it is not only the contents of the message that is responsible for the change but also the simple existence of a work of prophecy based on messages from the future.
It seems to me that in a multiverse theory you are not really traveling in time, it presumes a more or less parallel existence of different worlds. You might travel back to your own past, but from there on you are not in your own history time line anymore. Multiverse theories avoid the time travel paradoxes as the consequence of your actions continues in an alternative parallel world. I agree that the multiverse theory could be used as a conceptional model to simplify thinking about the effects of time travel, but it is not likely to represent reality.
The strongest argument against a multiverse theory is that it would allow future scientists to change the past without consequences for their own world, effectively giving them some kind of test-world. A future time machine could send time travelers to the past and change the outcome of historic events. As a test case they could make Napoleon win the battle at Waterloo or give Hitler an atomic bomb in 1940 and observe what the consequence would be. If there would be no risks or consequences for their own present, time travelers would be quite open and extreme in their actions and a receiving world would have a good chance of finding out the presence of such future time travelers. This however does not seem to have happened in our reality.