While hysteresis is expected in cybernetics, I suspect that time in the ordinary vernacular is a construct of the nervous system, and as such it doesn't make much sense to talk about a "brain" being temporally behind because the "present" is purely a construction.

There's science demonstrating that the part of self awareness that experiences causality of one's own actions is delayed relative to the initiation of the action, along the lines that the initiation of choice and the awareness of choice are reversed, with the awareness lagging the action, even as it feels like the awareness must cause the action.

So there's a temporal gradient in the totality of the human nervous system with respect to attention.

Anyone can experience this directly by trying to listen to what you say as you say it. It is to one's sense of personal causality something like trying to gaze at yourself in a mirror, while hearing a recording of your own voice. Self gets mushy.