Photoshop Elements 13 problem in keeping it out of my photo albums

I have been trying to understand your question for some time, and the result is that it only makes sense if:

- your photos are not 'opening', which would mean 'opening for edition in the editor', but appearing as thumbnails in the media space of the organizer;

- and if you have set your preferences to automatically search to register photos in your catalog via a preferences setting: the 'watched folders'.

To check this, in the organizer, go to the menu File >> Watched folders... and if the dialog shows different folders, remove them.

It will help if we can agree about the difference between catalogs and albums as defined in Elements.

Catalogs:

https://helpx.adobe.com/elements-organizer/using/creating-editing-catalogs.html#about_catalogs

Albums:

https://helpx.adobe.com/elements-organizer/using/creating-albums.html#about_albums

To make it simple, a catalog is just like a paper catalog: a list of files showing their location and properties as well as thumbnails for visual search, with a number of indexes for multicriteria searches. You decide which photos should be managed (known) by the catalog. You download from cards or import files already on your disks. The 'watched folders' service scans your computer as a background task to find if new files have been written in your computer externally.

https://helpx.adobe.com/elements-organizer/using/local-files-cds-dvds-video.html#using_watched_folders_windows_only 

Albums are just like playlists for audio files: lists of files managed in your catalog (possibly in your own custom order).