I have Jenkins version 1.480.3 installed on my machine and Email-Extention Plugin 2.30.2.
Test mail from \"Manage Jenkins\" section works fine. When I add editable email
It appears that, in some version Extended E-mail Notification become own SMTP Server configuration. So check your configuration under "Manage Jenkins" -> "Configure System" -> "Extended E-mail Notification" and make sure that fields "SMTP Server" and " Default user E-mail suffix" are filled properly.
Make sure also that the configuration is consistent with "Manage Jenkins" -> "Configure System" -> E-mail Notification.
TL;DR
Fill out fields "SMTP Server" and " Default user E-mail suffix" under "Manage Jenkins" -> "Configure System" -> "Extended E-mail Notification"