authorship - Supervisor partially putting themselves as first author even though I've done most of the work and written most of the paper

I've completed a project in computational physics. 100% of the code and running of the code completed by me and the introduction, theory and code description in the paper written by me. Results section written by supervisor with some feedback from me.

When we put the latex together I was listed as first author on the paper, since, as my supervisor stated, I did 95% of the work. However, when the paper was submitted my supervisor listed themselves as first and corresponding author in the online submission fields (I was still first in the author list of the submitted paper - ie. in the actual latex document).

When I pointed this out to the supervisor they denied it, so I logged in to the journal account and sent a screen grab showing the status, They said that they must have made a mistake and would correct later when resubmitting (flagged for some missing documents).

Later on I got an email from my supervisor stating that they had submitted the documents but 'forgotten' to correct the author status but not to worry because I'm listed first in the submitted latex paper.

I'm not sure what to think here. Perhaps my supervisor is correct and it will make no difference (since I'm listed first in the latex paper) and is just winding me up. Either that or not I feel that I need to push back here, somehow without damaging the relationship.

Addition: I think perhaps the author list inputted in the online fields may be used for citations but the paper itself will have me as first author. So perhaps my supervisor wants their name to be that cited?

Answer

The first answer to this question suggests that this might be incompetence rather than malevolence. A second (and to me more likely) possibility is that it's neither malevolence nor incompetence, but simply bureaucracy.

Your description is confusing and it seems possible that you misunderstand what's happened here. With many journal submissions, there's a series of boxes where you enter authors' names and information. These boxes are not necessarily related to author order! You can enter names in any order you want and it's completely irrelevant to the actual published author order. Often the first box is for the corresponding author, who is not necessarily the first author.

From your description, it sounds like this has happened. If so, probably the reason your advisor is so casual about this is that it's completely trivial; it has no bearing on your concern. The author order is the order in the manuscript and you're worrying about something that's not an issue.

It's also possible that the advisor thinks this has happened but the order is relevant, but from the way you've described it that doesn't seem to be the case.

A bigger issue, to me, seems to be your relationship with your advisor. Even though your advisor promised you first authorship, reiterated the promise, and assured you that the issue would be corrected, you've leaped to the conclusion that they are trying to "steal" your authorship. If you mistrust your advisor to this extent, is this a healthy situation? Has the advisor done anything to justify this immediate and very harsh reaction, or is this a case of paranoia? It seems to me that the answer, either way, is likely to have a much bigger effect on your career than an apparent minor misunderstanding.