Inside a balloon there are gas molecules (oxygen, nitrogen, etc.) bouncing around and exerting pressure toward the outside of the balloon. If the balloon was not in a vacuum the gas molecules from the outside would be exerting pressure toward the balloon surface, opposing the pressure from the inside. However, there is no gas in a vacuum, therefore any pressure. So yes, you are right. The balloon exploded because of the lack of pressure in the chamber causing the balloon to expand, releasing pressure from inside.