[[WMG: The Time Devourer will be the next story arc's Big Bad, after Alex takes care of the current Big Bads]]
The Time Devourer has been stated to exist 'outside of time and space'. Thanks to the way the story is set up, all the worlds that Alex has visited are connected, much in the manner of Kingdom Hearts, including the future of Chrono Trigger, Chrono Cross. Which means that the Time Devourer exists outside all of their times and spaces too!

Besides, wouldn't it just be ''that'' awesome to have the Time Devourer as an overarching BBEG?

[[WMG: The real reason Alex has been pumped full of darkness is to [[spoiler:turn him into a spare vessel for Xehanort's True Organisation XIII.]]]]
Maybe [[spoiler:Xehanort]] thinks he can form an advantage by acquiring somebody from the real world who has knowledge of the oncoming path, or capturing the very Interference who can spoil his plans and turn him in favour of completing them.

[[WMG: Because of Kronos' extremely sloppy armour theft, Aqua will end up being dragged into [=TI4=].]]

[[WMG: At the end of [=TI3=], Lucca and Alex actually [[spoiler:made out behind the throne room.]]]]
So they both appear [[spoiler: out from behind the back of the chair with massive grins on their faces]], huh...? Not to mention, they'd clearly been there for some time long before the others got there, and they both seem to [[spoiler:consider themselves as an out-and-out couple when Ed teases them later, without even a moment of hesitation, when previously they had been ridiculously embarrassed to talk about it]]. Lucca doesn't even mind [[spoiler:being talked about as 'the girl']].

I'm going to suggest there was some funny business involved.