People describe what they want done to guns in all sorts of ways. When I saw the title of this post I was going to suggest marking the finished length in Sharpie to prevent misunderstandings, but that’s a little late.
Machinists and gunsmiths have to be exact in their questions, interactions, and cuts or they aren’t in business very long, but that’s hard to do even in a perfect world. I’m guessing between you and your brother something was said that gave the smith the impression you are talking about receiver to can length - obviously you didn’t intend that, but I doubt a smith would screw up 4 measurements without a good reason. It could be something as innocent as you saying you like the looks of a 16” barrel - that could be interpreted as the visible portion should be that length.
The exception to this is minimum legal barrels - many smiths won’t cut a barrel to 16”, but it will be somewhere between 16” and 17” - usually they will tell you.
Worst case, he’s a drunk or on pills, or has old timers, or just got done beating up his wife or kid and wasn’t thinking straight.
I doubt he has enough extra margin to be able to recut every barrel he works on and stay in business, so there’s a good chance he wouldn’t recut them for free.
That’s a bummer.