I think that's a lesson for all of us, whether they have addictions or not. We should be more sensitive about telling any STBX about the other one. I try my best with this, because I still like my brothers XW, and of course she is the mother of my nieces and nephews, so I don't share stuff about my brother with her, nor do I share stuff about her to brother and new wife.
I think it's just so new right now for you L.O.T., but you should set the ground-rules with SIL soon, so it doesn't become a pattern for her to run to you with all the details. I don't think she would be offended if you just explain your side. Something like, "I am not very comfortable hearing about things STBXAH (that's a long title) does, and I am sure that he would feel the same way about hearing stuff about me" and if you look all of that up in the dictionary, it means ZIP IT! (don't add that part, even if you think it!)
Does Miss Manners have a website? This falls more into her category on things ppl should/should not do or say.