Interestingly I have flight out with IB on 9th July from LHR T5 to MAD. Then back from MAD to LHR on 12th July - which is the supposed move date. The BA app still lists the terminal we are returning to on 12th July as T5. It has not changed or been updated to T3.
If they have already updated the late July flights, then not sure why they wouldn't have done the same for early/mid-July flights. So not clear what the actual move date for this is from the info in the app at the moment.