Hello David
Great experiment! It truly sheds light on the inner workings of these STP timers/aging mechanisms. Indeed, the documentation you shared states it very well:
The age timer starts at the message age that is received in that configuration BPDU.
So if the age timer begins at message age, which is a value of 10, then it will reach the max age of 20 in 10 seconds, which is what you saw in your topology. Your experiment gives greater understanding of this statement, thanks for sharing!
Laz