DFC is very correct.
If you can find a picture of the internal workings of the Turn Coordinator, all the better. If not imagine a tyre sitting up with the gimbal system attached to the holes in the wheel and springs below this. Crude I know
OK... the gyro spins (say away from you) and an aircraft enters a left turn...the turn is felt as a "push" on the gyro (thinking of the tyre its felt at the 3 o'clock position - now looking at the tyre from the side) through precession (because the gyro is spinning) the system feels the push at the top (12 o'clock). This pushes the gyro (tyre) down and to the right, and through gears the needle goes left.
I hope that made sense.
Now, as the aircraft speed is incresed it takes more initial push for the precession to show the same amount turn on the dial. The only way for you to increase the precession is to increase the angle of bank (which is what you have to do with an increased speed for rate 1).
So it does not sense the speed, but rather the new force and resultant precession as a result of the increase angle of bank for the speed.