Minnow can you give a link to one of the job postings? Sometimes job postings mention incumbent because there's someone already in the position or sometimes the incumbent is the one doing the hiring. Also, sometiems the duties listed are those of the incumbent, as an example of what the work might be like (but they also might be hoping for someone who can expand the role). Without seeing the job listing(s), I can't give much more help. Here is how incumbent is used correctly, though:
Yet when a search involves an incumbent (i.e., someone who
currently occupies the position for which you are searching and who
will be replaced by the person you hire) or an internal candidate
(i.e., an applicant who is already employed by the institution, but in
a different capacity), the complexity of the process increases
exponentially.