sorry, I tried to reply before, but something on the website messed me up...
The first one is correct: you are always ON and island, and always IN a state.
so: you could correct the second one by saying "I met her ON St. Simons Island, in Georgia."
Oh and btw, I liked your question better as it was earlier; even if the island is not connected, being IN a state is a political definition, so the island will be IN Georgia's borders whether it is ON the mainland or not. Unless the islanders are thinking of secession