Great question. I would imagine that it's simply the tree adapting to the climate: perhaps entering dormancy earlier and more deeply, hardening off earlier (adjusting to shorter seasons), maybe even changing some of the characteristics of the type of growth it puts out. Added to it is the fact that the tree is older, has a stronger root system, and older (and therefore stronger/hardier?) wood.
I don't think its DNA is changing, though it's possible that it, from time to time, produces mutated branches (sports) that have characteristics that differentiate it from its parent. I don't know how common these "sports" are among figs. I have a calamondin tree that just produced a variegated limb this past year.
Perhaps a more seasoned botanist/gardener can speak to what's truly happening physiologically?