I have two instances of civiCRM, both versions 4.7.30, both running under Joomla 3.8.5.
On one instance, I can select the recipient groups and see the items selected... In the other instance, the Recipients box isn't behaving the same -- if I try to select groups, I don't see them in the list box afterwards, and the Recipient count always reports "No Recipients".
Both instances have public mailing lists, with positive Contact counts.
civicrm/admin/setting/url?reset=1
andcivicrm/admin/setting/path?reset=1