Could it be that Chrono Trggers are the things (people, machines, what have you) that cause the dimensional splits. Whatever decision or indecision they make creates a new timeline, and likewise a new dimension.
Think of it this way, you have the Lavos timeline. Then Chrono and Co come in. That screws with whatever happens with Ayla and Kino. Their coming could ensure the fate of humans, or as in a New Game + ending, destroy our hope, letting Reptite's rule.
The same could be said of Serge, Kid, Time Devourer and everything. Serge is a Chrono Trigger. His actions directly affect more than one dimension. Thus, it is more than right to name him the Chrono Killer or whatever he was called (been awhile since I played this). His actions kill many of the different dimensions and futures that Chrono and company create.
Granted, Serge's actions also can create different timelines as well, since now Schala (Kid) is time traveling searching for Serge... What I find funny is that we know she saves him in 1010, so why doesn't she travel to 1010 and save him, and then come back to the exact time after Chrono Cross is finished? But whatever on that one.
What you also have to consider though is what the world will really be like now that Chronopolis is gone, FATE destroyed, and Dinopolis a never. Would Lynx even exist? Would Serge still exist? And moreover, if there's no Serge, would Lucca be around? The possibilities are truly endless, as are the plotholes, and new dimensions ripped open by Serge and (the much too large) company.
I could go on for hours about the consequences of choice, action, and chrono triggers, but for now, bed... that is my choice.
