Welp, I don't want to ruin anybody's fun, but there's a few things to consider, most of them not exactly hidden within the story.
There's the fact that we have no evidence whatsoever that the original Starkiller's soul or what-have-you survived his death (and in case anyone cares, the aforementioned novelization makes a case against that belief).
Then there's the presence of the cloning facility itself. The Starkiller we follow in the story was grown in a vat. For whatever reason, he's being tormented by the original one's memories, but that isn't evidence that he's special, since the other clones all went through the same thing. The only thing that sets this one apart is that he actually managed to escape Vader (his predecessors probably made similar breakout attempts, but failed).
Furthermore, that cloning in real life does not give copies the memories - or even skills - of the host is irrelevant, since cloning in fiction virtually never works that way. It certainly doesn't in Star Wars, as evidenced by the clone army seen in the prequels and a few other odds and ends from EU sources.
I don't ever remember the clone troopers(who become stormtroopers) having to deal with memories or flashbacks with Jango Fett. So, its not something natural, but most likely something Vader did to him. How that was, I haven't a clue!
My personal theory is that cloning gets exponentially more complicated if Force-sensitivity is involved, such that for whatever reason, clones of Jedi have some sort of link to the original's memories (since as you said, Jango's clones seemed fine).