"Pistonic motion" does not.
To be fully accurate: at a high enough frequency most cone drivers eventually have break up modes where the driver no longer functions as a piston. It is the speaker designer's job to account for this in picking the driver and low pass filter.
There is no "true piston" vs. not designation in traditional drivers, just what range and what output levels they remain pistonic in.
The exception that proves the rule though are the Ohm type drivers, which are decidedly NOT pistonic. I believe they are fixed at one end, and driven at the other.