I am saying that it is not a national procedure, as the AUS controller told you, and that it isn't something that is normally done.
The local technique has apparently conditioned at least that one AUS controller to think that this is a national procedure. Its regular use at your home airport conditioned you to think so as well. What happens when such a pilot is departing from an airport somewhere else where the controllers don't routinely remind pilots of the ODP? Will he know that it's his responsibility?
I've seen this conditioning affect many times over my career. It is very common on all sorts of topics. Pilots tend to "do what my CFI did" without thinking about why it is being done. That student "grows up" to be a CFI and teaches his students the same thing, still not knowing why. It becomes "tribal knowledge".
There's a great story that the late "Bad Chaz" Harrell (sp?) told in his Effective Mental Conditioning lecture, back in the 1980s/90s, about an examiner who kept getting private pilot applicants who would taxi at a high RPM dragging the brakes to control their speed. When asked why, they'd say, "Because it's good for the motor" but they couldn't explain it any further. I won't ruin the punchline but it was something that had been passed from CFI to student down the chain for many years without any of them know why. When he traced is back to the old, retired CFI who originated the chain, it was for something that no longer applied to modern aircraft.
Here's the whole lecture. It's very good. I don't remember how far into it the "because it's good for the motor" story is.
In the late 1980s I was a flight instructor at a very busy towered airport that had an aviation university flight program plus three additional busy flight schools. It wasn't unusual for 10, or more, aircraft to be in the pattern at the same time. Some of the controllers had developed the habit of instructing each airplane to report downwind abeam the tower on each circuit. "Make left closed traffic, report downwind abeam the tower on each pass". It wasn't all of the controllers who used that technique, though. Others, in my opinion better, controllers considered it a crutch and would only use it when there was a good reason for it; not routinely. Afterall, when you have 10 or 12 airplanes in the VFR pattern, do you really need extra radio calls tying up the frequency?
Pretty soon, everyone had been conditioned to make that report regardless of whether or not the controller had asked for it. Since everyone was making it anyway, many of the controllers who relied on the report would often leave out the instruction to make it. Didn't matter, right?, as everyone's making it anyway. Now what happens when a transient pilot comes in and doesn't know that the controller is expecting a report that he was never told to make?
Another affect was that many of the pilots would fly their upwind, crosswind, and first half of downwind with the expectation that they wouldn't be interacting with ATC until they made their "abeam" report as that's how it had always worked. That's were the controllers would usually give them their sequence. The result was a higher rate of missed calls for pilots who hadn't reached the mid-field abeam point in the pattern. Many simply weren't listening yet.
Lastly, I'd take my students to a nearby non-towered field for landing practice and you'd have other airplanes, based at the same towered field, making position reports of, "[airport] traffic, [callsign], left downwind, abeam, touch-and-go". Abeam what? There is no tower to be 'abeam' of. "Abeam" had become a synonym of "midfield". A midfield downwind report isn't even one of the recommended reports to make at a non-towered field.
That's the appeal-to-authority fallacy. Just because he should know, doesn't mean that he does. His position still has to be backed up with facts and, in this case, it is not.
Always track it back to the source. The FARs, AIM, ACs, 7110.65, etc. Those are the real authorities. Those of us with more experience can often be helpful in pointing you in the right direction, even if we are wrong ourselves. But never accept our opinions just because the person giving it 'should know'.