There is no such thing as self-plagiarism.
If you have written something and the journals allow it and are aware of
it, it is neither illegal nor prohibited by academic standards to
publish and recycle it in 100 journals if it is your work.
I think you mean some other problems by the term "self-plagiarism":
- The author tries to sell his old work as new results obtained by
paid work. That is fraud,
pure and simple, especially if the author was funded to get new
- The author has published the work under the copyright terms of the journal. Normally the journal gets exclusive rights for publication and
violating this terms is illegal.
Even if it is not forbidden, people do not try it except for a very good reason.
You are aggravating your academic colleagues because place for publishing is precious and you are wasting this space (There is nothing against trying several publishers as long as you retract the other submissions). You are also indicating that you are past your zenith in your academic career if you need to fall back on old work (In fact, I think of it more as terminal illness) or you come off as having a massive ego problem if you try to push your invaluable contributions into several journals. So your indignation is justifiable, especially because Journals will normally not allow duplicate publication and your suspicion is legitimate.
So contact the journal editor of the first publication and clear that up. It may be perfectly explainable what the author is doing, so take no action until you know what is going on.
ADDITION: Just for curiosity: PLL's "But it’s well-established now with the meaning of “re-using one’s own old work and presenting it as novel”" convinced me to ask Goggle's Ngram because I was curious about its usage.
So the current usage in books is 45/100 000 000 instances.
If we compare that the usage of the domain-specific, non-English word "Camellia"
Camellia occurs (at maximum) in 40/1 000 000 instances. Which means that "Camellia" is used approximately 100 times more than the "self-plagiarism" term. For fun, "Camellia" is comparable in usage to "trichloride".
It was used sporadically during the 1990s ("Duplicate publication" is definitly preferred) and only after the 2000s it became more prevalent and also used in titles and abstracts.
The Wikipedia entry defined "self-plagiarism" 2005 and there it was specified later that this word was used mainly by biomedicine to summarize four categories: duplicate publication, copyright infringement, salami-slicing and use of own text modules. It must also be said that its usage is controversial for exactly this reasons,because it tries to subsume salami-slicing and the use of own text modules under a term which contains much more serious violations like duplicate publication or copyright infringement. So "self-plagiarism" is according to the "Committee on Publication Ethics" not equivalent to duplicate publication.
Sorry, but "self-plagiarism" seems to be neither as widespread or well-accepted as claimed nor is its usage uncontroversial.