The date the FX rate applies is the "settlement date", which is the date on which the merchants processor is paid by the issuing bank processor. Many people, including here, offer precise dates on which that takes place, but in fact there is no precise date because time lags can happen between merchant, merchant processor, network transmission, issuing bank processor (if applicable) and issuing bank. Usually all that happens very quickly, often in a single day or two, but not always and not consistently. Time zones, cutoff times, holidays and other factors intervene to reduce consistency.

Even so, as you observe, credit card FX rates, assuming no DCC and no FTF, are virtually always far better than a consumer can get elsewhere. Ditto for debit cards. Between Visa, MC, Discover and American Express different procedures apply. Discover does almost all theirs through a large bank, Royal Bank of Canada, IIRC, while American Express does their own in many countries and use local partners in a few of them. Visa and MC have long standing procedures that generally are quite consumer-favorable. Still everyone makes money in this process. There are exceptions: for example, Argentina has horrible rates because the central Bank sets an artificially low rate for all official transactions, thus almost all regular travellers use cash that they buy through an unofficial market. Those exceptions are not common these days.