I hear what you're saying, Myself.
I actually asked her if she was referring to body touch and she said not at all, simply an awareness of one's own internal experience, hence the term 'somatic' experience.
I have given the matter some thought, and I believe I have some clarity on it now. Here's an example: One time my T told me to do something (some kind of behavioral intervention). She then asked me 'How does that make you feel?" And I was able to access the experience of feeling 'controlled', her telling me what to do felt controlling to me. I believe this is an example of getting in touch with my internal/visceral experience in a given situation.
I think I will ask my current T if she would be ok to provide this kind of frequent checking in with my somatic experience, so that I may gain greater self-awareness.