What version are you running? The bindings look different in the latest version (2017.3.1) and I see they populate as I would expect to the extended type.
This seems to be a Bug but we found a Workaround.
After Adding the Field and the Relationship go back to the new link field. Activate "commonly used" and save.
Afther that, the Bindings are still not shown on child CIs but if you use the new field in Child CI Form, Control Type ist correct shown as "Link Field".