In the English Grammar Profile, C1 point 19 in CONJUNCTIONS/coordinating is defined as:
inverted auxiliary ‘do’ + the subject after ‘not only’, to give focus.
For example:
It‘s kind of like the dirty, little secret of poverty, which is that, not only do poor people take in very little income, but also, the income that they take in, they don’t spend it very wisely, and unfortunately, most of that spending is done by men.