I have heard the following: True they didn’t leave until the next morning, but because they had brought the Korban Pesach on the fourteenth which the day which a person brings a Korban is a personal Yom Tov and prior to Matan Torah our days started in the morning and were followed by the night (as opposed to after Matan Torah when the day begins with the preceding night) therefore, that night was actually part of their Yom Tov and cooking for the next day was prohibited as it would be prepping on Yom Tov for after Yom Tov.