JPGs have also non-image data which reveal used equipment, applied software, used settings and many other technical things. That's called metadata. If you have made adjustments in Camera Raw to a JPG, the adjustments are listed in metadata.
If you have selected Camera Raw preference "Open JPGs with settings", Photoshop check the metadata and opens in CR those JPGs which have already got something in CR.
You do not need to save the image in CR, the adjustments are inserted to its metadata automatically if the file isn't write protected. You can see its "last modified" -timestamp changes. The metadata is updated when you exit CR. Exit by Cancel does not cause metadata update.
If you in Photoshop save your file with File > Save As, a totally new file is generated and it naturally hasn't CR adjustment list. That's because those adjustments are applied to the image data irreversibly when the new file is created. CR adjustments listed in metadata are only a receipe, the original image data stays intact in CR.