ON1 Photo RAW is fully non-destructive, and stores your edits and other changes each time you move between modules or images to the programs' database by default. There is no need to actively save your work between images or modules. You can also configure the program to save your non-destructive edits to sidecar files, as well. Click here for more information on how to enable sidecars in Photo RAW.
Please note, because your edits are stored non-destructively within the program itself, they will not visible when the image is viewed outside of the program (such as in File Explorer, Finder, or another processing software). In order for your changes to be visible outside of the program, you will need to export them first.