There is no 1-2 second delay tho; bitcoin transactions take 1 hour to confirm. At best, you might have 7 blocks between receiving, sending and being credited on the exchange.
Of course, this is possibly things like Litecoin are more stable as you can 'get in and out' in 15 minutes.
This was merchant payments. Essentially bitpay guaranteed the USD you would get at the point the transaction occurred. They didn't send the USD, that happened a day later.
So buyer pays in btc, bitpay handle the transaction, probably sell the same amount on an exchange at that point, tx confirms and they pay out the USD. The BTC then goes into the bitpay reserve for the next merchant.
Of course, this is possibly things like Litecoin are more stable as you can 'get in and out' in 15 minutes.