Interesting problem, one I have not come across before. I am thinking that what is happening is that the pump is staying on after it drains from the was cycle.
Try this, make sure the pump has stopped and start the machine with the rinse cycle. If the machine fills, try replacing the pump. If the machine drains out, then it sounds like the timer is activating the pump as the rinse cycle begins and the timer may need replacing.
If you buy the parts from this site and they do not fix the problem you can return them.