Is there a potential problem when an academic supervises a Ph.D. student in a very specific area in which someone close to them is also active and working (and supervising Ph.D. students who are publishing in that area) at a different institution? What if the two students are producing very similar work, at the same time? Is it right that my alarm bells are ringing?
I can think of multiple sane reasons not to publicly state romantic or marital involvement with a fellow researcher. There surely is no obligation to do otherwise.
Now, in the situation you described in your comments, you mention the possibility that one adviser is leaking unpublished results of her/his students to her/his spouse's students without the consent of the person who did the work. This is indeed problematic, regardless of their marital status.
If you are worried about this situation, discuss confidentiality with your adviser, make sure you are on the same line and consider sealing an informal agreement of non-disclosure with her/him if deemed necessary. This can be independent of the spouse situation.
One potential conflict of interest is if both were acting as reviewers for papers or grants submitted by each other, or if they were members of the hiring committee that evaluated each other's application. Since married couples have a reciprocal interest in their spouse's employment and wealth, there would be a quite probable conflict of interest.
It's not considered a conflict of interest for an advisor to personally work in a field similar to his/her students' - it's expected.
It's also not a conflict of interest for an advisor to have friends working in a field similar to his/her students' - it's likely.
Similarly, it's not a conflict of interest for an advisor to have a spouse, child, or immediate family member working in a field similar to his/her students'.
The exception to the above would be if the advisor actually does something that harms his/her student in order to favor him/herself, a friend, or a family member.