A rollover object has two parts.  You may not be selecting the correct part.  Select either the rollover hit area or the object that appears on rollover, then go to Properties and look for the button that allows you to specify audio for that part.

If the audio is attached to the overall object's HIT area then that audio will start to play as soon as the object enters the timeline.  If the audio is attached to the caption that appears on rollover then the audio will only start to play when the caption is visible.