Pressure plates send an 'open' command when something steps on them, and a 'close' command when something steps off of them. If a pressure plate sends an 'open' command to a door/floodgate/floor hatch that is already opened, nothing happens. The only exception to this is gear mechanisms, which toggle their engaged/disengaged state on every trigger from a lever or pressure plate.
In order to build a timed sequenced mechanism like you device, you will need to build logic gates and timers using water logic. For example, you have the first pressure plate open a door that lets water into a sealed chamber. That chamber contains both a pressure plate set to trigger when the chamber has water in it, and a pressure plate set to trigger when the chamber doesn't have water in it. The pressure plate set to trigger when water is not present is linked to the doors in and out of the drowning chamber, and will close the doors and hold them closed when the trap is active. The pressure plate set to trigger when water is present opens the floodgates to let water into the drowning chamber.
When the drowning chamber fills up with water, it activates a pressure plate that starts the timer. The timer can consist of a long corridor that water is let into from one end, with a pressure plate at the other end. When the water reached the other end of the corridor, it will open a door to your sealed chamber described above that will close the floodgates letting water into your drowning trap and open the doors to the drowning trap, letting the water out of it in the process. You will also need to have a mechanism that drains water out of the timer to let the system reset completely.