But note that although the "rate of aging" is a coordinate-dependent quantity, the actual amount of aging that a twin will experience on his path between two points in spacetime is not coordinate-dependent. It will be the same no matter which coordinates we use and what coordinate-dependent rate of aging those coordinates suggest. The key here is that although the "rate of aging" will be different in different coordinate systems, so will the "time" during which this aging is happening, and the two effects always balance out to give the same total amount of aging along the journey.The "rate of aging" of a twin is a coordinate-dependent quantity. In the inertial coordinate system of frame A, T2 ages slowest afterward. In the inertial coordinate system of frame B, T1 ages slowest.
[Of course stevendaryl knows this already. I'm just trying to stop someone else who doesn't know this from being confused by this aging-faster/aging slower right now thing]