This happens because you instruct Acymailing to send it twice.
In Configuration->Subscription you have enabled Require confirmation. Because it's enabled Acymailing send out a confirmation mail to all new subscribers.
Aditionally you have a script running that contains code to send a confirmation mail. It's probably in the plugin you have created. Otherwise check if you have runn ing any other scripts. Just remove the code that send the confirmation mail. Because of the setting in the configuration Acymailing takes already care of it.