My interpretation of this is that the Hacker and Spider (or Firewall) make an opposed test that takes 1 minute, not just 1 action. If the hacker fails, he is free to try again, but with one less die as per the extended test rules.
This is correct.
The decker is free to stop after the first interval (after each interval actually) or probe for another interval, but with one less dice in the pool (while the opposing dice pool is unchanged). Possible adding up more net hits for the backdoor entry test that follows. But also if any probe interval is not successful (or if the following backdoor entry test is not successful) then the whole extended probe attempt fails and you have to start over from scratch.
I think you only compare AR and DR once at the beginning of the whole extended test. Also that you are only allowed to spend edge once on the whole extended test. That the whole probe attempt count as "one" extended test, no matter how many intervals you spend on it.
Mathematically you are often better off just probing for one interval. Which mean you can often treat it as a regular opposed test that take 1 interval to complete.
is this actually spelled out somewhere ...
It is not clearly described in the book, no :-/
The idea is that Matrix Search follow a similar pattern.
But this also suggests much higher threshold values than presented in the legwork table.
If you wish to keep the current legwork table without modifications then you might want to treat matrix search as a simple threshold test that take one interval to complete.
(edit: slipped by MC)