I not following. If nothing is open in Photoshop and you select files in the bridge then use menu tools Photoshop>Image Processor. Photoshop should open the Image Processor Dialog for you to fill in and hit run. When you do the files should be process one at a time. Open changed new file saved and document closed. There should never be more the one document open at a time unless you include an action which opens and closes files.
Have you tried not including an action just have the image processor resize. Have you tried running the Image Processor from from Photoshop and not use the bridge. Process either open document or point it to a folder of source images. The Image processor should process one image then move on to the next. You wrote all images opened. With normal processing only one image should be opened at any given time.
The message with a list of files must be coming from some script and the message about feather I can't see the Action step fot the palette is hidden by history palette.
Your actions should also be simple not do any resizing. Set the Image Processor to do the resizing that is one of the scripts main features.