In contrast, Proxima Centauri orbits from a distance of about a quarter lightyear, and we've found a single planet orbiting very tightly. We've also found a single planet around Alpha Centauri B, also orbiting very closely. There may be more we haven't found, but probably not nearly as many as in the Firefly system. Firefly seems to use the idea that more stars mean more planets, but more stars and planets during formation means more chaos, more things to swallow up or rip apart planets, and more mass to throw them out of the system.
I don't think the Firefly system is necessarily impossible. You can even construct models such that the white star is at the focus of all other orbits (you know, if you're the Alliance and you need to do that for political reasons). (An Earth-centric model of our solar system needn't necessarily be wrong in terms of its ability to predict the position of bodies in the solar system - It's just needlessly difficult and convoluted.) I just think the Firefly system is highly improbable.
The 'systems' in Firefly are really all one star system. The system includes a central star orbited by planets, four other stars, and a host of "protostars" (they really mean brown dwarves). I've tried, and can't imagine a scenario where, even if such a system could form, that it could be configured in this way. The barycenter of the masses of this system can't possibly remain in the central star indefinitely, for starters. And the whole thing sounds hostile to planets - I imagine them being thrown out of the system constantly. But if you accept that, and you accept travel at some fraction of c, then you wouldn't expect them to age much like they would traveling between systems.