One possible explanation is that the input is picking up a stray signal (output signal, or some other internal signal path).
A buffer acts as a voltage follower and ensures that it's output (and in turn the input to your Tyrian circuit) closely matches its input, so whatever interference is being induced back into your Tyrian input is subdued by the buffering.
Fire up the Tyrian, set it so it's oscillating nice and loudly, and see if touching the input wires has any effect on the oscillation.
Also two questions:
- What kind of guitar / pickups are you using?
- What overdrive did you use in front of the Tyrian?