Amex has always used a call center in India, especially handling calls during off business hours. They are actually pretty well trained and I've had more or less good luck with them understanding my requests, compared to other companies with offshore call centers. But they aren't perfect.
In the grand scheme of Amex cards, I don't believe the Delta Reserve is treated as the same tier as their high end Platinum self-branded cards (despite similar annual fees), so it doesn't surprise me they route calls for it to their ordinary call centers.