Thing is, it probably wouldn't clarify anything even if i asked him "what do you mean by 'everything is ayumi'". He'd show me examples (again) and explain (again) but I can't really get all the nuances and be able to relate it in English until I have more experience.
Anyway, I'm not sure the OP was really asking about a specific technique like irimi. I wouldn't say to call "walking through" "ayumi". It just seems to be the term we use for what she was asking about.