OK... not too difficult a concept here. If you have enough amplifier, the amplifier will reproduce the wave form as that wave form is presented to the amplifier. This will permit the driver material to move in and out in a normal and natural movement. For the sake of visualization, imagine the driver moving to a 1kHz sine wave -- it goes out, it goes in, it goes out again, it goes in again... lather, rinse, repeat -- the amplifier isn't causing the mechanical part [the driver] to move in an unnatural manner.
Now -- imagine that same wave for where there is an insufficient power amplifier... the net result will be a "clipped" wave form. Instead of the natural "peaks" and "troughs", the waveform will move up - hit the point of "clipping" -- smooth out the top of the wave into a line [causing the driver material to stay stop and stay stationary for a bit], then as the wave form recedes, the driver will once again follow its path back to the "center" line -- and have the same "herky - jerky" motion on the bottom side of the waveform.
This creates heat. When the driver doesn't move in a smooth in and out motion, heat is created. Heat is the mortal enemy of any driver element. With the exception of Piezo tweeter elements, driver technology is all based on magnets, and electrically charged elements... be they the ribbon in a ribbon tweeter or the coil that pushes a woofer or compression driver -- its all about the electricity that travels through the charged element. That charge will be positive or negative -- which will relate to the positive or negative charge of the surrounding magnet. If the charge is similar, the the driver moves out... if the charge is dissimilar, then the driver moves in -- if the charge is a flat line [as in the case of our clipped signal], it forces the driver to hold its position [which they don't like to do, and that's what causes heat].
Heat, over time, will break down the insulation on coils... which leads directly to driver failure. The only time you can run into problems with "too much power" is if the driver's coil gets pushed out of the gap [due to too much power creating an over excursion of the driver's coil... and that coil doesn't come back and seat itself properly], or you can pop the ribbon element [again, and over excursion thing].
If neither of those events occurred... then your driver elements are fine.
I hope I explained this clearly... please feel free to let me know if I have done an insufficient job for your comprehension of the way these things work.
Peace