In all chips, higher voltages are correlated to higher frequencies. There is no way around that, it's physics. Voltage is what pushes the on/off (0 or 1) in all stages of a CPU. Not enough voltage? Your data becomes corrupted as the CPU doesn't understand a 0.5, 0.25, 0.33 (only 1 or 0). Again physics of transistors and how logic gates are built.
That said, efficiency is related to how the pipeline of execution works in a CPU. How much work can be done on 1 W of power. That means you can do more with less. In other words if the M2 would be clocked exactly as the M1, voltage and hence power consumption would be the same (relatively) but work output would be better than M1. However, as the M2 works faster on its higher efficiency, it can consume less power, but in order to achieve that faster speed a higher voltage and hence power requirement is needed.
All that happened is that the efficiency gains of the architecture allowed the M2 to be a 5W chip vs a 10 W chip (throwing numbers to illustrate the point). In actuality, the wattage will increase proportionately as voltage increases as clock increases.