I don't believe the time is all that critical. No flooding and drining do not happen at the same time. There are lots of ways to do this, but the simplest way is with auto-siphons that kick on at a pre-set level and rapidly drain the system, then shut off. In all the systems I've seen the only common factor is draining the bed to allow air to get to the roots.

In most of the systems here, people slowly fill the bed, then rapidly drain it. In the barrelponics system the bed is rapidly flooded, then drains just about as quick. The max flood level should be an inch or two below the top of the media to prevent algea growth.

Check stucco's system Expansion for a typical bell siphon setup.

http://www.fastonline.org/content/view/12/26/ is the barrelponics website.