Parts of thesis draft published without proper credit
Your instructor has committed serious academic misconduct several times: if it is your words or your work being published, you should be one of the authors and your permission is required for publication. It's also not clear from your post whether the same material was published multiple times, which would also leave you vulnerable to accusations of self-plagiarism.
It sounds, at least, like you are no longer working with this instructor, which is a good thing. You should always look to separate yourself from seriously unethical people, lest you be tainted by association or involvement in their crimes.
Now you are faced with a problem of cleaning up a toxic mess, because your instructor has also lied to you about this "not being a problem" for you. There are three different aspects of the cleanup that I can see:
What should you do in your thesis? I think that your supervisor's suggestion here is good: put in a footnote at the beginning that explains where else the various pieces of the chapter have been published (both with and without you as an author), and note that due to misconduct on the part of the other author, you were not listed as an author. Note that I am assuming the instructor is not required to sign off: if they are, this may be a problem.
What should be done about the papers? Once you are safely graduated and are secure from retribution in another position, you can contact the publishers and request to have the record corrected. The note, signed off in your thesis by your supervisor, will be useful here. If material was inappropriately reused in multiple publications, you might instead ask for some of the publications to be retracted. Don't be surprised, however, if the publishers fail to take action, as many publishers are not very responsive when asked to correct the record.
What should be done about your instructor? It is very difficult for a student to accuse their instructor of misconduct. Fortunately, it sounds like you have informed a responsible senior individual (the tenured supervisor), and it would now be appropriate for you to pass the responsibility of deciding how to proceed to that person. Unfortunately, it sounds like this person may not actually take any action, so you may wish (again, once you are away and secure from retribution) to contact people who actually have authority over the instructor and may be willing to act.
Finally, be prepared to simply walk away if you need to: fortunately, this is happening only at the Masters' stage, and so all of this mess can likely be rendered irrelevant by your future work as long as you take precautions (like the note in your thesis) to avoid it coming back to bite you.
In addition to jakebeal's fine answer, I want to note that this problem would have been entirely avoided if your instructor had simply included you as an author, as virtually all publishers allow published journal material to be "recycled" in master's and doctoral theses, and vice versa. (It would make life exceedingly difficult for graduate students if they couldn't reuse material from work published during their careers in their thesis!)
The other issue is that you should maintain a paper trail of all of your correspondence with the instructor regarding the papers that were submitted (and I hope you did maintain such records!) Without them, all of the allegations will be much more difficult to sustain, as it will become an "X said, Y said" allegation.
One other thing to inquire about: will your university offer you an extension on turning in your thesis? Many universities allow students to petition for a short-term extension (usually a few weeks). If so, then this might give you time to revise the affected text to remove the plagiarism allegations. This might be the best option for you to avoid future problems.
Too long as a comment so I am submitting as an answer.
While I like the principles of jakebeal's answer, I would like to advise against citing someone committing a misconduct in a permanently archived document without a proper investigation. I am sympathetic about your situation but to any future investigation committee you're simply another party of interest, and it's fully likely for you to accuse the other of misconduct. That's drawback number 1.
Drawback number 2 is that the world comes and goes around. Just because the instructor is no longer in a position to harm you does not mean he cannot do so in another occasion. If you've decided to use the footnote approach, I'd recommend saying a human error was made rather than a misconduct was committed.
This is not to say I would always cover for unethical people, this is to say that without a proper third party's investigation, I will not accuse anyone especially if I am involved in the issue.
And I also think rewriting, as suggested by aeismail is also a good approach if you don't feel like hurting the instructor in any way.