Telling PhD supervisor I published a paper about my thesis without telling them or listing them as authors?

The answers here are generally explaining the fact that supervisors should not be omitted from the authorship as they are supposed to direct and contribute to the research.

The critical problem is, you are saying that they did not contribute at all, and they, naturally, did not write or review the published article. Still they try to add their names as authors when they learned about the article submitted. You can not be an author if you did not even review the article, just this information is sufficient to see that the ethical misconduct is mostly on their side.

Your problem is, you can not both submit an article without making "such" people authors and at the same time maintain a good relationship with them. A one-author paper is, for me, much better than giving credit to the people who disregard the functioning of the academy, by both hardening the situations unnecessarily and also making academic misconducts. Even if you somehow get your advisors' names added to the paper, they will never ever forget this. At the same time, you shake the ethical ground of your publication by this act of "correction", and it may, in the end, cause the rejection to your paper. All the while, you will still be considered untrustworthy by your advisors, quite rightly in their perspectives.

Your only choice is to forget about updating the author names, and find some other ways to correct your relationship with the advisors.

And please keep in mind that in academy, at least in Turkey, almost everyone faced in a situation that more than the bulk of work done by someone and just because their advisors don't like them they don't give authorship to the corresponding researcher. And these advisors made their Ph.D. in top-tier universities of USA. I think you will most likely face such problems from now on.

The real issue here isn't about communication with your supervisors; it's about academic misconduct on your part.

In this post, we consider exactly this issue: given a supervisor who required 32 drafts over 4 years (!!), the [now former] student wanted to downgrade the supervisor to an acknowledgement so as to submit the paper without requiring their approval. The verdict was unequivocal:

If he deserves to be an author based on his intellectual contributions to the paper, then it would be unethical to deny him authorship based on being difficult to work with

This is precisely what you have done -- denied authorship to someone who deserves it. You may not feel they deserve it, but this is not for you to decide -- by agreeing to collaborate with them on your thesis, you agreed to work together and co-publish any results. You can't unilaterally decide their contributions were worthless after the fact.

In this post, we consider the inverse situation: a professor taking credit for his students' work without acknowledging them. As the answers show, this behavior was completely unacceptable, but it's difficult for students to seek redress when professors misbehave. Unfortunately for you, it's rather easy for professors to seek redress when students misbehave.

So, what should you do? I would start by understanding what your options are. Is there any way to prevent the article from being published? Can you retract the article? Assuming the supervisors contributed to the work, could you publish an addendum saying that authors were incorrectly listed? Then, you should take these options to your supervisors. Tell them that you understand you had no right to publish thesis-related work without their inputs, that you regret it deeply, and that you will address the situation however they want. You should probably make other plans for letters of recommendation, and also think about what you will do if they refuse to continue working with you.

Edit: Since I wrote this, OP has claimed that the supervisors made no intellectual contributions to this work at all. If this is truly the case (and intellectual contributions don't just mean working on the manuscript!), then this might not rise to the level of academic misconduct. But, the supervisors will be (rightfully) angry that OP has been doing (and publishing) thesis-relevant work alone, after (implicitly) agreeing to work with the supervisors -- OP's best option is still to find a way to undo this submission and give the supervisors a chance to earn authorship.

To add on to cag51's answer, chances are the editor is being careful about changing the author list because situations where authorship was purchased have happened before. One can guess how it's done: the original authors submit the article, it's accepted (or accepted pending minor revisions), and then during the next stage they amend the author list. Superficially, from the editor's point of view, this seems like what you're trying to do.

It's likely that the journal will let you amend the author list, but only if you give a thorough explanation of why you need to change it. Tell them the added authors are actually your supervisors. Prove it by using your institutional email address, giving your supervisors' names, and their official institutional websites. You can copy your supervisors, too, using their institutional email address (this is arguably a good idea in any case, given the academic misconduct). You may be asked about what each author's exact contributions were, so prepare a response.

You can't change the past, but you can change the future. Making genuine, good-faith efforts to fix the mishap will go a long way towards fixing your relationship with your supervisors.