Alright, I'm going to have a shot at deciphering this mysterious turn of events myself, starting with Eclipse Magus.
Who is Eclipse Magus? Where did he come from? Is he from the future, or an alternate dimension?
This is one of the most debated questions thus far, and one of the reasons for this is that most people haven't tried beating the game without recruiting Magus yet (which is understandable, as it's so fucking tempting).
However, I was able to keep another save file handy for this exact purpose, and I can tell you that the same events happen even if you've killed Magus. This is supported by his dialogue both in English and in Japanese in which he says that he doesn't know if he's from your future. But it is quite clear that he defeated Lavos with Crono and his party, thus he is the Magus that left the party during the standard ending (#1). Therefore, I have come to the conclusion that his origins are completely up to the player's performance: if you opted not to fight him and obtained the standard ending, congratulations. You have encountered Future Magus. Otherwise, he is clearly from another dimension, and this is the dimension that is carried on into Chrono Cross. The fact that Magus acknowledges infinite possibilities and thus, infinite dimensions confirms that the #2-12 endings in the game are indeed existent in their own right...but nothing that you need to trouble yourself with because the sequel is based on the canon endings #1 and #13.
I notice one of you is insisting that he could have created another group for this purpose, but why muddle the plot like that? You're only overcomplicating matters. There's no evidence supporting this, anyway. The reason for the Prophet disguise is to make it clear to the player that he is not the same Magus that they've encountered. If by some chance I left him out of my party when I went to Time's Eclipse, if Eclipse Magus didn't have robe on I probably would've assumed right away that my Magus got a headstart.
Did the party truly encounter Dream Devourer and Eclipse Magus, or was that a plot device?
My only response to that is, "Does it matter?" They had no effect whatsoever on the outcome anyway. I'd like to consider the possibilities that they did and didn't witness the events that transpired, as they're both explicable. However, I'm leaning more towards the possibility that they did witness the battle, because should you perish at the hands of Dream Devourer, you still get the "FUTURE REFUSED TO CHANGE" cutscene.
Party never witnessed it: Kato is displaying to us that Magus surviving is the canon ending, and that this is what happens to him after his departure. Try as we might to stop Dream Devourer, this is the way of things as already seen in Chrono Cross, and there's nothing we can do about it. The party being there is merely symbolizing the player being able to see the events after 13 years of wondering what happened. We get our answer, and nothing more. Schala sends us away, effectively saying, "Show's over, folks! You want to save me, then boot up the sequel and use the Chrono Cross, don't bother leveling up...not that there are levels in CC anyway."
Party witnessed it: Another interpretation of the events to come is that the "Entity" really wasn't at rest after Lavos's defeat because of the events in motion surrounding Schala becoming the Dream Devourer. With the fall of Guardia (and thus, the deaths of Crono, Marle, and Lucca) imminent, the planet -- or rather, all of time and space -- is facing extinction. So, the Entity creates the dimensional vortices to warn our party of the impending events, thus empowering Crono, Marle, and Lucca and finding out Dalton's plans.
With the heroes's strengths at their absolute peak, the Entity believes they can battle the Dream Devourer. Crono's party arrives and saves Eclipse Magus, buying him enough time to recover, despite him not wanting them there. Once he recovers, he sees that the party has failed as well, and saves them from being destroyed. Perhaps there's a part of Magus that does care for them? Or, maybe he just doesn't want them to get killed because if they're from his past it could negate the defeat of Lavos and he wouldn't want that. Either way, Schala regains herself momentarily. Accepting her fate, she first removes Crono's party as they've seen enough, and erases their memories of the dimensional vortices so that they won't "dwell on this" and defeat Lavos as they would have anyway. I like this possibility because in saving Magus from being outright killed by the Dream Devourer, it's possible that the party is responsible for the birth of Kid, as it could have been this moment that Schala decided to create her, and the birth of Guile, if it turns out that he is indeed an amnesiac Magus. Although, that would sound a lot more appealing to me if Guile had a more prominent role in Chrono Cross...
Regardless of whether the party saw it or not, Magus, following his defeat by Dream Devourer, is soon being tormented by the same despair that seeped into Schala's heart when she wished for everything to be erased (probably also because of Lavos's influence). She got her wish, and Magus got his -- once he entertains the notion of erasing everything that he is and leaving something new behind, that's exactly what happens. It was most likely Schala that granted this during her brief moment of clarity, as well. It could be because of this that Frog regains his human form, as well.
Anyway, I think I'm done here. There's my interpretation of all this.