Going back to the OP’s question. I could be wrong, but here’s how I see the path the people in your example took to arrive at what you consider a reversal of logic. Whether taking that path was right or wrong...who can say? It's a idiom.
“I got to the mountains by way of the tunnel.” Basic use of the phrase according to a number of dictionaries.
In that regard they could say “I got to this neighborhood by way of that city/state.” So NOW, “I’m from the mountains (the neighborhood they now call home) by way of the tunnel (their previous city or state).”
“From the seashore I got to the mountains by way of the toll road and the tunnel.”
In this regard, they are living in the mountains or they are from the mountains (now), but they got there by way of the tunnel, the toll road, and the seashore. Question is, in what order do you list these locations? Did you use the toll road before or after going through the tunnel? This could cause confusion if you’re trying to lay out your whole life and all the places you’ve ever lived. But if you pick your original starting point and your ending point, eliminating all the ones in between, you could say:
“I’m from the mountains (where you live now) by way of the seashore (your original starting point).”
At first glance this may seem ‘backward’, but the people in your example aren’t listing a travel itinerary or a biography. They’re answering the question: Where are you from (or consider yourself to be from) [now]?” The ‘now’ is implied. “I’m from the mountains and I got t/here by going through x.”
Someone who has moved from one place to another a lot, may not consider themselves to be ‘from’ their birthplace. In which case, when the question “Where are you from?” is asked, they don’t think “Where are you from [originally]?” Instead, they think “Where are you from [most recently]?”
In the example from Mad Men, the Illinois-born character came to Atlanta directly from Pennsylvania and considers himself to be from Pennsylvania (but he got there by way of Illinois).