I can’t imagine what may have happened but no, this is not typical functionality of the Duplicator plugin. There is a video overview that you may want to check out: http://lifeinthegrid.com/labs/duplicator/
The process is to install the plugin on the site to be moved ( domain A), create a package & install file, copy the package & install file to the new site ( domain B ), and run the installer. The info that you enter into the installer determines where things get moved around to so do you happen to have a screenshot of that or remember what was entered in each field?