This is not exactly true.
There is always a balance, regardless of time. On a physiological level, the balance depends on the pattern of motor unit recruitment, which is in turn primarily determined by intensity of the force output and the gradient of oxygen available to the muscle fibres. On a molecular level, the balance depends on the kinetics of each of the processes relative to the rate of ATP energy demand (including availability of oxygen/glucose etc). Anaerobic metabolism is favoured during short, high intensity bursts of activity, simply because it is faster at producing ATP.
Maximal force (~8 seconds) will consuming the energy already stored in ATP and creatine phosphate in the cell. Maximal force for ~30-40 seconds will also utilise stored glycogen in an anerobic manner as well as a modest proportion produced through aerobic metabolism, since some of the pyruvate produced through glycolysis will be fed into the citric acid cycle (and in turn, oxidative phosphorylation), at the same time.
Maximal force for these time frames is much higher than can be maintained for longer time frames. Past this point, force will drop off and aerobic (ox-phos) metabolism will contribute a larger proportion of the energy. After hours (the exact amount depends on intensity), the glycogen stores in the muscle will be depleted and the individual will "hit the wall" unless they stop or slow down to a level of activity that can be maintained through replenishing glucose via circulation and through fatty acid metabolism.
But we are far from maximal force when doing the dishes, or walking around the block, hence when doing these activities, a much greater proportion will be due to aerobic (ox-phos) metabolism.