There are many levels of "dumminess" in english/russian translations. This one is very thin.
However in my opinion phrase "Это был обычный день для ... , пока ..." whispers that it is direct translation from english. As was said above, there is nothing wrong. But, imho, something like "В тот день ничего не предвещало..." or "Для рассыльного то был обычный день..." sound "more russian".