Water Supply Tube to Icemaker Freezes Up?

The white plastic insert that marries the water line from the solenoid to the back of the freezer (Kenmore icemaker kit IC6 factory installed in our refrigerator/freezer model 596.68142891) is pushed away from the unit by water pressure as the filler tube freezes up inside the freezer.

This has happened twice. The first time I defrosted the unit and turned it back on; the second time I turned it off. What is causing the filler tube to not drain properly which leads to the freezing up?

Thanks.

By VZ