Camille Landry said:

I am only working with 2 TMs : a main TM that is the only one being updated, and another one that I use as reference, but never update. They are both in the same language pair. 

This might not be the case, but since you're not updating your second TM, is it possible that the old translations you're seeing are actually coming from this TM and not from the one you're updating?

No, I don't think that's the case. I have never updated anything in the TM that I use only as reference (I use it because it's updated by my colleagues and can be useful occasionally to search through for inspiration, although it never provides significant matches unless it's for single words). 

However, I've finally noticed something that I did not mention when I wrote my original post : the segment duplicates only occur when it's a different user who confirms the segment. For example, I seem to be able to overwrite my own confirmed segments. But, if I work on something in Trados, then confirm the segments, save the file on a server and fully close it (off of Trados Editor & Projects), and then my reviewer opens my own file from my server on her Trados on her computer later on, and edits then confirms her corrections, the TM will save up both my old translation and her new one, instead of overwriting my previous translation after she has edited and confirmed. Essentially, my TM will memorize different versions of a same segment from the same file, if it was confirmed by one user and then edited and reconfirmed by a different user.

Is that supposed to happen and is there something that can be done to prevent this, or make it so that other users can overwrite other people's work like they would with their own work? 

Thank you for your assistance!

No, I don't think that's the case. I have never updated anything in the TM that I use only as reference (I use it because it's updated by my colleagues and can be useful occasionally to search through for inspiration, although it never provides significant matches unless it's for single words). 

However, I've finally noticed something that I did not mention when I wrote my original post : the segment duplicates only occur when it's a different user who confirms the segment. For example, I seem to be able to overwrite my own confirmed segments. But, if I work on something in Trados, then confirm the segments, save the file on a server and fully close it (off of Trados Editor & Projects), and then my reviewer opens my own file from my server on her Trados on her computer later on, and edits then confirms her corrections, the TM will save up both my old translation and her new one, instead of overwriting my previous translation after she has edited and confirmed. Essentially, my TM will memorize different versions of a same segment from the same file, if it was confirmed by one user and then edited and reconfirmed by a different user.

Is that supposed to happen and is there something that can be done to prevent this, or make it so that other users can overwrite other people's work like they would with their own work? 

Thank you for your assistance!