Hello
I have just been in this situation, and this is my experience with changing Tier mid trip with AA. The basics of my trip was that I landed in Honolulu on a Friday and it was that flight to HNL that would push me into silver. My routing had been DUB-LHR-PHL-PHX-HNL with the last two legs on American. I was due to fly out of HNL four days later on the Tuesday.

After landing on the Friday the American flights posted to my BA account within 48hrs. By Sunday evening my time in Honolulu my status was now silver on the BA app. I was very pleased.

However my happiness was short lived. When I got to HNL I checked into my flight to LAX and when the kiosk spat out my boarding pass it still showed me as a oneworld ruby (BA Bronze). When I spoke to the agent checking in my bag I raised this with her. She stated that the AA computer said I was ruby not a sapphire. I offered to show my status on the BA app but she declined, stating she had to go by what was on her computer. Then asked if I wanted to pay $50 for lounge access, I declined.

The next day my connecting flight back to London was on BA, no issues there as you would expect. I even had the CSM coming up to me on the flight telling me well done for obtaining silver. So I was wondering after BA shows you as silver does it take some time to filter down to the other airlines in the alliance?

Brian