Nice find! Seems like the random number they use to check against the Quick Claw activation chance is actually just shared between every Pokemon holding Quick Claw at any given time.
Good eye! This was changed almost two months ago when DaWoblefet updated end of turn effects for Gens 5-8. I spent a few days checking Gens 2-4 and updated them at the same time so there wouldn't be any regressions: https://git.io/Jc6bMhey, recently noticed a change in the end-of-turn mechanics in ADV on pokemon showdown.
You're right that it's intuitive since almost every effect in the game for the last 10 years has been done for the faster Pokemon first then the slower one immediately after, before moving on to the next effect in the list. A commonly seen exception is Grassy Terrain and Leftovers both happening for a faster Pokemon before a slower one. In Gens 3 and 4 exceptions like that were actually the majority of end of turn effects, though.and couldn't find any discussion on this in my 2 minutes of searching, just wanted to know if this has been tested because how it worked before makes more intuitive sense to me. It seems pretty rare that this would be impactful to an actual game.