I don't really think there is a right or wrong way to do it. I do tend to be hesitant to explain it to people, but I really think it is just my TMS goodist personality coming out. I either don't want to offend anyone who may have chronic pain or I don't want to be considered "Psycho". But to a certain extent thinking this way, in my case, really only perpetuates the TMS traits that caused my symptoms in the first place. A large part of recovering is accepting the diagnosis and the strong emotions that we have been repressing. I think learning to tell people about TMS is part of this, because, at least in my case, in means that I simply accept that I had TMS and realize there is nothing wrong with it.
Still, when I do explain I usually use the term stress instead of psychosomatic. I also really like how Sewmuch said she explains it "I solved my stress induced muscle pain through a retraining program and making adjustments to my lifestyle."
If someone gets it great, but if they don't who cares. I'm pain free and that's all that matters!