How relevant is it, if updates to a journal paper are not reflected on third party websites?
It depends on the third party website. If they are constantly monitoring the main journal, it might happen, but I would assume that this is not true for every website. On the other hand, in most cases the journal should only be available via the journal web site thanks to the copyright regulations of that journal. And people citing the work should always look for the original source.

Therefore I would say it is not a problem of your friend, maybe it can be a problem for people working with unreliable sources. But I would not care.