I imagine that around the time the mission specialists were to be woken up, HAL would have played the recorded message from Dr. Floyd to Bowman and Poole, thus bringing them up to speed. The world found out about the Monolith's existence from Bowman's transmissions anyway. Either the mission planners didn't think through how Bowman and Poole were going to be briefed, or they didn't inform HAL on when there were to be briefed and he started to become more and more paranoid that they might find out about the top secret mission that he was not suppose to tell them about because they were getting close enough that they might actually see it if they looked at Jupiter with a telescope. His instructions were written wrong, as seen in 2010 when Dr. Chandra pulls HAL's orders, but did HAL have orders to tell the command team of Discovery about the Monolith?