Apparently East Asians have more neanderthal DNA than Europeans so I'm not sure the region of initial discovery really matter that much. Also Neanderthal 1 is 40000 years old, your family may have arrived in the region even a 1000 years ago and be completely unrelated to it.
It works the other way too though. There's a good chance that at some point along those thousand years, somebody had kids with somebody else who had older ancestry in the area, and so on.
