Molting is a normal process where the bird substitute part of its old feathers for new ones. Having said that, it hardly means getting naked exposed skin.
I am not familiar with cockteils but I know that budgies and zebra finches don´t have strong molts. They can loose feathers the whole year in a "lesser molt". Considering that both are native australian species and the cockteils are too, I could expect a lesser molt for teils too, which is quite different of what is shown in the pictures. Some members that have teils can help more regarding the molt subject.
Have you considered your cockteil may have parasites that are itching that area?