From your use of prefixes, I suspect you’re using SPM as your preprocessing pipeline? Just so you know, fmriprep (the tag on this post) is a separate preprocessing pipeline (see Chris’s links). I have very little experience with SPM, and it has been many years, so assuming that is what you’re using, I can’t help with the specifics of the tool. However, I can make a couple comments:
I’m not entirely clear on what all SPM does; it should not modify the original files, but it does change them in some way (probably an updated header, but I haven’t actually looked into this). But yes, the new files should be the preprocessed variants.
I am wondering if the slice timing must be performed after realignment or before.
Slice timing correction, if performed, should be performed before coregistration. Once you interpolate your image, the slice information is at least partially lost, and the assumptions of any slice-timing correction algorithm will be violated.
Related: Obtaining movement estimates before slice time correction