Miles would've left the island because Chang was warned by Daniel's coming back about the upcoming Purge. He wanted his son out of it even if he himself was doomed, so he somehow sent him off-island. At least, that's what I would do. So if that's it, then Miles grew up off-island raised by someone else (maybe named Straume.) And maybe the name-change was for his own protection -- Chang didn't want anybody tracking him down, so he arranged for an adoption and name-change. Again, that's probably what I would do.
I would say the age is about right, isn't it? Isn't Miles around 30, give or take? And Dr. Chang's Barracks Video (with the baby crying in the background) says it will be seen "about 30 years" in the future.
Jin has exactly the right age (born in 1974) an was raised by someone who doesn't know if he is his father.
A woman, that looks a lot like Candle's wife, brought him to mr. Kwon.
But the first time I saw Miles I thought he was Candle's son, because he really looks like a younger version of Candle.