Check out this interesting closed question; my name appears twice. I voted to close before made moderator pro tempore, and again afterwards, and my name appears in the list twice because of that. It's a very minor bug which admittedly will happen pretty rarely, but it should at least be on the bug report list.
This isn't really a bug, as Shog9 notes - you literally did vote twice. This is acceptable because we're not going to go back and undo all close votes of a user when they are promoted to moderator.
Consequent to that, a moderator's ability is not to vote to close, but to simply close - this is thus unrelated to whether or not you had voted on the question in the past. It's not as if your vote "counted twice" because you already could close it in one shot to begin with.
While it does come across as amusing behavior, I'm of the expectation that this isn't something that truly needs to be changed because it is non-impactful and also, as you note, relatively rare in occurrence.