Normally the tube is full of air, but the pickup is just a pinhole to allow water into the tube. As speed increases, the water fills the tube above the pickup, thereby pressurizing the air in the rest of the tube. As you slow, the pressure in the tube overcomes the water pinhole pressure, so the water is forced back out.

So, you're correct in that normally the speedo sees no water. But, if there is a hole in the speedo diaphram, then the pressurized air in the tube blends out through the hole in the diaphram...until there is no air left. Then the diaphram fills with water, and finally that pressurized water leaks out through the hole in it.