But how does he calculate this? He's not some sort of time travel expert, he's just a "simple miner". How would he even know where to begin to calculate the exit point from a black-hole-induced time jump? It seems like it should be way over his head.
There could be a million reasons. Maybe he studied it with the help of his computer. Maybe someone in his crew knows about it, like an engineer. Or maybe he himself is knowledgeable on these things, but never pursued a job in that field. It's not really that farfetched.
At this point it's either Fantasy or Sci Fi...this is either a massive plot hole for the sci fi factor or the story is utter fantasy.
Well, since Science Fiction is a sub-genre of Fantasy I can't see your problem.
I don't think so. While they overlap quite a bit, sci fi generally tries to explain things with science or reason, where fantasy just calls explains things by saying it's magic.