My advisor submitted a paper with my work without including me as an author

It is an unambiguous violation of ethics for a collaborator to be dropped from the list of authors.

If you wrote a significant contribution to the paper, you are in the right. Your supervisor has no ground to stand on. You should ask your supervisor (don't accuse!) if he/she has included you as a co-author. If a mistake has been made, the sooner it's fixed the better. You could also have a good claim to first authorship, though that is something to decide between authors.

Edit: a little humour - full credit goes to Nik Papageorgiou / The Upturned Microscope.

There may be nothing to worry about. In ScholarOne (the web submission system being used), the submitter is supposed to enter contact information for all the authors, but an impatient submitter might skip that. As long as you are listed as an author on the paper itself, I'd bet the web submission stuff can be fixed after the fact (it might annoy people, but it's unlikely to derail publication). Probably the person you called at the publisher just checked the ScholarOne metadata without examining the submitted PDF, in which case you don't know for sure whether it lists you.

Instead of provoking an angry confrontation, I'd focus on first figuring out whether you and your advisor are in agreement on authorship. I'll assume you have not explicitly discussed this question, since if you had, then you should have ended up with agreement one way or the other, or at least known you disagreed.

As a first step, you could bring up the question. For example, you could write "I realized recently that we never explicitly discussed authorship of our paper. I've envisioned myself as first author and you as the senior author, since I wrote much of the paper and it is based on my thesis work. However, I should have discussed this with you before submission. What's your take on the author ordering, and how did you handle it in the submission?"

Then you can decide what to do based on her response. If she explicitly says you're an author, then I'd trust her on this. You could still discuss author ordering, based on the conventions in your field.

If your advisor says she doesn't think you should be an author at all, then you'll have to discuss this issue. It would be counterproductive to accuse her of dishonesty or of trying to steal your work. Instead, you should just try to make the case that your contributions justify coauthorship. You could refer to guidelines for this journal or for your field in general to help you argue.

Yes, web submission software can send authorship confirmation emails to all co-authors, but not all journal publishers actually configure it to do so. I can confirm that at least one journal by Taylor & Francis does not send confirmation emails to people other than the corresponding author.