Transistor as a mute switch, odd rise and fall times?
The fall time begins, when the voltage between the base and emitter reaches ca. 0.65 V. During the fall time the voltage between the base and the emitter does not change significantly, only the base and collector currents are increasing.
That's why the capacitor does not increase this time significantly.
Your capacitor introduces mainly the delay time (between the moment when the voltage goes high on the microcontroller output and the moment when the base-emitter voltage reaches ca. 0.65V and transistor starts to conduct).