Outside North America (though this offer is only valid for select European hotels, majority being UK), all charges are processed "at the hotel". There is no problem with any rate, including semi flex and advance purchase, because they are all charged in the same way.
Even hotels.com would work if paid at the hotel (paying hotels.com online won't because you are paying Expedia which doesn't send your Amex number to the hotel).
I have always received the credit as long as my Amex was charged within the offer dates, including on prepaid stays which are for long after the offer ends.
The offer is also cumulative and works on attached shops. For example, a £3 daily coffee from Costa at Hilton Olympia for 67 days would trigger the credit.
Ah really! That’s good to know - I assumed the fact that it specifically says In-store only on the offer it means it has to be one of the non-advance pay rates.
Thanks for clarifying!