In order to use dependent fields you must have Power Scripts™ for Jira app installed and enabled.

For the moment, dependent fields can only be used by the two custom fields with autocomplete.

Starting with Power Custom Fields PRO™ 4.0.0, you can use the dependent fields on SQL data sources as well.

In order to get the value set on the screen for one custom field, reference it like this: "argv[customfield_id]".