2019 Photoshop Elements is automatically exporting images from Photo Editor to Organizer

Glenn has probably given you the best answer.  But your post is a little unclear.  So, let me add that when you are saving a file in the Editor, a checkbox exists in the Save and Save As dialogs to add the file to the Organizer.

It doesn't actually export anything- organizer monitors the folders you tell it to monitor and creates a "shortcut" to the folder which includes a thumbnail, and available metadata associated with those images. 

Files (the thumbnails) often become missing when you manually move or delete the files outside of organizer.

In organizer you need to look at FILES>WATCH FOLDERS  There is an option to turn off automatically add files to organzier.