Use of the word "issue" as a euphemism for "problem"
Solution 1:
"Could you make clear when to use "issue", and when to use "problem"?
The simplest answer is this: when the best word to use is issue, use it; when the best word to use is problem, use it.
I think (along with others in the above comments) context should guide you. Here are two examples, one "correct" and one "incorrect," of how the two words can be used.
Correct:
"An outstanding issue from my perspective concerns the frequency with which people generally use the word issue as a euphemism for the word problem."
Incorrect:
"In my opinion, people who insist on using the word issue when they should use the word problem have issues!"
In other words, there are times when issue is the right word and problem is not; and vice versa. I think the providers of the guidelines would recognize the differences between the two uses of the word issue.
Solution 2:
Since the journal doesn't provide a rationale for its guideline, I can only guess at what its reasoning is, but I suspect that the distinction it is trying to enforce is between matters of contention or controversy ("issues") and difficult puzzles that are in need of solving ("problems"). Obviously these two categories of things overlap—but they don't overlap entirely.
Earthquakes are a serious problem in many parts of the world, but they aren't an issue in the narrow sense of that term because no one seriously advocates on behalf of a pro-earthquake position. Conversely, the status of John Brown in U.S. history is an issue (because it sparks heated debate among both experts and nonexperts), but it isn't a problem per se. The overlap occurs in areas where something like HIV has aspects of a problem (the need to find a cure) and of an issue (controversies over funding for research, treatment of sufferers of the disease, and public education aimed at prevention).
It seems to me that the journal might offer these definitions for "problem" and" issue," in contrast to the ones that you identified:
problem: an intricate, unsolved question
issue: a vital or unsettled matter that is in dispute
In other words, the journal probably doesn't view "unsettledness" as a common feature of both "problems" and" issues," as your dictionary-based definitions do.
To avoid running afoul of the journal's policy, I would limit my use of "issue" to matters involving controversy and active debate. I would not use "issue" to refer to undisputed problems. In making this recommendation, I don't mean to endorse what I take to be the journal's line of thinking; I'm interested here only in suggesting a way to understand the distinction it appears to be making.
Perhaps the most ironic aspect of its guidelines is the fact that the journal evidently doesn't instruct writers not to use "problem" as a synonym for "issue."
Solution 3:
The journal you're submitting to appears to dislike the use of "issue" to mean "problem". In other words, they disagree with the dictionary, and think the two words should not be synonyms. (It happens: language is under constant change, and those of us who speak it all resist that change in some areas, and embrace or even cause it in other areas. A good dictionary will list all common definitions of a word, even those that are controversial.)
You have two options: you can either avoid the use of the word "issue" entirely (unless you're talking about an edition of a periodical or some such), or you can try to draw a distinction based on whether the particular point under discussion can be considered a bad thing (in which case you must use "problem") or not (in which case you're OK using "issue").
In practice, of course, it's not always easy to determine whether an open question is a bad thing or not — sometimes, you need to know the answer to the question to determine that, and then it's no longer an open question. This is where all the other synonyms of issue/problem come in useful. :)
Solution 4:
"Issue" has pre-empted "problem" in the vernacular of people who are in psychotherapy. Today it serves as an indicator of who is in therapy or at least a significant other of someone in therapy. ;-) I have no idea how it came into vogue to such an extent. I have been living abroad for 30 years and these changes (other examples are "I'm good" or starting every sentence with "So ...") hit me like a ton of bricks every time I return stateside.