EDIT: To answer your question more directly, you are steering in one direction to initiate a lean in the opposite direction. E.g. if you are attempting to turn right, you first steer left which generates force in a left-sided contact patch in the front tire, which causes the bike to lean right. The bike then assumes a stable right lean angle (you have to do some work with your body, but the bike naturally wants to do this), and the front wheel comes back into alignment, and you are now turning right.
A good explanation: https://www.youtube.com/watch?v=PgUOOwnZcDU Some more detail: https://en.wikipedia.org/wiki/Countersteering
EDIT 2: I misread your point. You are correct, counter-steering still applies at low speeds but the "feeling" is masked by lack of momentum.