When the machine is started the timer tells the inlet valves to open and let water in. As the machine fills the air pressure in that tube you blew into increases and when it reaches a certain level it causes the water level switch to engage, which then send the signal to the timer that the tub is full, so the timer will stop the water from coming in and start to agitate.
As you may have gathered from my earlier posts, I really don't know if your problem is the water level switch or the timer and you should do what I would do if I were there. Try both and figure out which one is the problem.
Yeah, not very scientific, but it works.