Actually it's a
wardrobe issue, Chakotay wore a Lieutenant Commander Provisional Rank Badge (almost?) the whole time if you can look carefully (not joking)... Rank badges have to sent out to be made, and probably cost at least a thousand for a speciality/custom construction gig... Studio prices are detached from reality ...While the property master alternatively has thousands of pips laying about the set, which is why Tuvok;s wardrobe malfunction only took SEVERAL months to remedy because his rank "talked about" did not reflect his neckline for all of season one.
Cavitt definitely was a Lieutenant Commander, who had the job before Chakotay, and since job dictates rank, then the XO for Voyager should always be a Lieutenant Commander and not a full Commander becuase of the ships capabilities, the amount of staff their is to manage, and the type of missions the ship is expected to embark upon, which clearly means that Cavitt's Voyager was a different animal from Chakotay's Voyager.
Field Commissions are real. they have to be ratiffied with command back home, but then all promotions have to be rubber stamped back home. They could have reinstated his old rank, but was Tom a lieutenant before he blew up his life?