Moving/Renaming images

Regarding the media library plus plugin. We have many images on an existing site ordered into year/month folders. We want to reorganize the images into five new folders. If we install and use the plugin, it seems that for every image we move or rename, we need to go to every page/post used by that image to recode the img tag to point it to the new image url. It seems the plugin does not update the mysql database automatically. Is that right? Thanks for your help.