Step 1: So how does a firepiston work, anyway?
The principle of increasing temperature by method of compressing air is explained by the Adiabatic process in which the internal energy of a gas must increase when a mass of air is rapidly compressed (or the volume of space containing a mass of air is rapidly decreased). The resulting increase in internal energy results in a rise in the temperature of air sufficient to light an ember, just like the pressure produced by an ice skater's blade is sufficient to increase the internal energy of the ice, which turns ice under the blade into water.
You can envision the effect in a 2D graph (below) with pressure as the ordinate (vertical) and volume as the abscissa (horizontal) and the adiabat or curve of constant entropy as the inverse relation curve. (Black lines are the curves of constant entropy.)
Rapid compression by a factor of 25 to 1 produces sufficient internal energy to send the air temperature to 800 degrees Fahrenheit. This temperature is sufficient to ignite a piece of char cloth for use in kindling a fire.
After several tries and some fine tuning (better sealing with more lubricant) I was able to produce embers with char twine using the apparatus I constructed.