3putt,
Your question got me thinking that I had saw the term adjusted alkalinity before. So I dug through a couple of books at work on disinfection/pH/Alk.
The only reference I could find was pretty long winded but it implied that a Alk measurement was taken twice, once from a representative sample (your water sample) . Then again after the pH had been adjusted to a known value in the test used it was pH 7, the alkalinity was then called "adjusted".
Sound like a load of POOP to me from a old book on water treatment, probably written by an engineer
I would just continue to do what you have been