The Network providers, i.e. Visa or MA sets the rate. As far as I know, the posting to your bank account is very close to real time. While I cannot know if it is instant, I know it would be no more than 30 min on the occasions I could check so soon after withdrawals. During our Transatlantic cruise last year, there were a few ports where I made withdrawals at banks near the pier just before returning to the ship. As soon as I got back to the ship, I went to internet cafe to check our account - the transaction was posted, in equivalent USD.
One thing I do notice, at least in Australia - the exchange rate tends to be LESS favorable, (or being jacked up), if the withdrawals are made right before weekend or banking holiday - i.e. the local banks which ATMs are used to make the withdrawal would be close for weekend or holidays shortly after the withdrawals. In 3 occasions, the rates were 1%+ higher than the historic rates reported on XE sites when I compared them.