So the actual idea here is that this small number of people said, "The End Is Nigh!!1!!!!!eleven!!!" and they corralled up a bunch of people who believed them. These people all then managed to get themselves to another planet somehow (manner not relevant) while the Earth behind them was effectively destroyed.
Your Event Predictors are going to be hailed as Prophets, most likely, and they'll be able to form their own religion based on whatever they want, so long as it incorporates some of the basic ideas of Christianity (because that's what they'll all be most familiar with). Everyone else will be True Believers, at least at first. Government would follow basically the same path. The Event Predictors will be assumed to have all the Right Ideas, so they'll have carte blanche to set things up how they want.
That's a pretty big ego trip, and they'd have to be pretty special, incredible people to not succumb to the temptation of power on that scale. Of course, they can also always blame things that go wrong on the rigors of adapting to a new environment, so the most likely outcome here is a sectarian oligarchy. Figure one of the Event Predictors will rise to the top through manipulation of one sort or another, and install himself as Leader-For-Life with religious and civil authority. Under him will be the other Event Predictors as a cabal of advisors.
How exactly they'd set things up is a matter of taste, but the basics are set. To begin with, the goal would be short term survival. Then they'd focus on settling in for long term survival, then they'd move on to find leisure pursuits. Tents + Hunter/Gatherer -> Houses + Farming -> Bars + [whatever]. Already having known life with electricity and computers, they'll seek ways to recreate that. Whether they have enough scientific knowledge to do so is completely your choice. Conspiracy theorists and those who can be swayed by them can be reputable scientists, they can also be crazy cat ladies.
I would expect splitting off to be minimal at the start. People busy trying to accustom to a new environment may bicker, but they'll stick together until they have time to breathe. It won't be until the Bars + [whatever] phase that there will be major splintering. I'd expect to see communities arise fairly quickly, though, wherein people form smaller groups out of the larger one, but it would be like neighborhoods forming in a city or suburb. You can only regularly interact with so many people, but that doesn't mean you want to get away from everyone else, it just means you have a set group you treat as trusted.
Major schisms would happen sooner, though, if you decide there are two or more people who fit the forceful, arrogant personality type within the Event Predictors group. If more than one really, really wants power and is charismatic enough to sway opinion, they'll create rifts, and people will pick one side or another, and you'll have multiple separate settlements. This will eventually happen over time regardless, as Machiavellian tactics get used within the Event Predictors, the sheep start to question things that don't mesh with their experiences, maybe people get taken advantage of and come to realize that, and so on.
Above all, keep in mind that the dissemination of information can be absolutely controlled, and it also cannot be controlled at all. El Presidente and his Cabinet can decide who gets to learn what and when, but gossip still moves faster than the speed of light.
That's my take.