I don't think anything about it was properly explained, and I don't think it ever will be. Honestly, giving any character an item as bullshit as this one opens up an insane amount of plot holes. There is just no way a random brat trainer, that is the protagonist, or his friends can even accomplish to do anything against a supposed omnipotent antagonist that can literally go to any point in time and do whatever they want to. It basically makes it feel like there is no point at all to the story that's being told. Either the antagonist is going to prevail as expected or there are going to be even more plot holes, because the only way you fight this type of bullshit is with even bigger bullshit.
Based on the explanations given so far, you can come up with millions of theories that would make as much sense as yours and whatever way the plot is actually heading, but none of them will ever be acknowledged or denied/given proper explanation on why they can't be true. To begin with, the introduction of time travelling to this story was, in my opinion, one of the worst things that could've happened to it. At this point in the story, the time mechanisms, including the magic warping crystals and these omnipotent tiempa, spacea and crescent beings, are very poorly explained and make the plot too inconsistent and senseless.
Time travel is not an easy thing to get done in story writing, so I'm not expecting a perfect story where everything is explained well and the plot headed the way it did because it absolutely had to. Convenience and light ass pulls are fine, but I don't think even these minimum requirements were met.