A substantial document nearing completion describes in detail how the data interface work is designed and implemented. Suffice to say that data is not converted to HDS, but that both FITS and HDS formats have been incorporated into the same logical data model and the operations by the application on that model map on to different ways of accessing the underlying files.
The main challenge of the FITS interface is not in getting one working, but doing so efficiently and and in a manner which does not require the way Asterix applications interface to their data to be radically altered.