We can't empirically verify that, is the thing.
We're told that the projection worlds we visit in X are places from far away being projected for our convenience, but 1) why would they have to be versions from the future, and 2) we see other characters teleport, surely the other worlds can't be too far away for us to get to, right...? The only thing we can verify is that these Disney worlds, which are based on real fairy tales and that MoM refers to as "stories", existed in a storybook.
Those Disney worlds then regenerated in the post-X world because the children kept the "worlds - stories" in their hearts. The children... who had only ever experienced them through a storybook, and were set up to do so by the Master.
So, the BoP pulls versions of the Disney worlds from the future, and the Disney worlds exist in the future because the children remembered them from the BoP. This, alone, is a closed loop. So did those worlds exist in the time of X? Impossible to say, and apparently has no bearing on the loop.