The logic doesnt sound alright. It is a fact that time and tide doesnt wait for anyone or rather it cannot wait for anyone whether he is on the move or stationary. For people who are on the move they may be considered to move in tandem with time and tide but time and tide still cannot be said to wait for these people on the move (constantly), its the actions (move) of these people which matched with time so to say, though not in absolute terms still.