The more I think about it, the more it makes sense. This could very well be an anthology series.
The first movie was obviously going to feature a giant monster, we always knew that.
I think with the small budget, it points to the majority of the film taking place in the bunker. That's what we've been shown. With the first film's teasers, we saw lady liberty's head fly into the streets of NYC, glimpsed the monster moving between skyscrapers etc.
This time, we see these individuals occupying this fallout shelter, passing the time, and we see MEW getting cabin fever, and attempting to escape. John Goodman is hell bent on staying put. That's the conflict at present.
The only connection it may have with it predecessor the vagueness of the situation at hand. We will only witness this group alone, and never cut away to some other folks in a different location. And we probably won't get much of the how or why. Just another mystery sci fi.
Or I'm over analyzing and it's totally set within the same universe and there absolutely is a monster outside, whether it's a sequel or taking place simultaneously as the first one.
Happy camper either way.