In my article, I have cited a preprint version (arXiv) of one references. After my article has been published in the final form, I received a request from the author of the preprint article asking me to make Corrigendum that tells the readers about the journal version of his cited article. I am new in the publication field and I want to know whether I should obey to his demand and make the corrigendum or leave the citation as it is. I might mention that the contents of both preprint and journal versions are similar and the version that I have read and referred to in my manuscript is the preprint as the journal version was not available at the time I wrote the paper. Thank you for your advise.
Is there a major difference (a grave mistake or something) in the journal version? Apparently not.
Is there a grave mistake in your paper that you cite a preprint? I don't think so.
You also cite the version you were working with, which is Ok and a right thing to do.
I'd correct the reference in my database for the future use (and obtain the journal version, of course), but I won't bother with corrigenda. They are for bigger mistakes than just a wrong version of a reference.
First of all, papers reference other preprints all the time, especially in my field where the submission to publication time is quite long. It would be ridiculous if everyone published a corrigendum every time a preprint you referenced gets published, especially because this is not an mistake. If for some reason journals allowed this, there would probably be more corrigenda than research articles. So, no.
That said, when you go through the final proofs stage for an accepted manuscript you should check the preprints you reference to see if publication data is available for any of them before your work gets published. (I can't tell from the question whether the other paper was published before you could make changes or not.)
No way you should have to bother about such bookkeeping. And it is not even clear that citing the journal version is the right thing to do, now or in the future, if you read and used the preprint version.
Nevertheless it is clear why your correspondent wants you to make the change: for bibliometric robots that ignore preprints, your article will not be considered as citing his. One more case of the publishing system asking scientists to do pointless work.