True bypass, well, bypasses all of the DSP and converters, including any mute and leveling. When true bypass is active in the PRE path, your signal is going straight from the IN [PRE] to the OUT [PRE] with only a buffer in the path.
If you've got Automatic True Bypass on, enabling the tuner should temporarily disable true bypass, since the signal is now hitting the DSP again. If that isn't happening, I think I'd consider that a bug. If on the other hand, you're activating the tuner and then activating True Bypass - see above. In true bypass, your signal is passed straight through.
Check your Tuner mute setting (on the CONFIG page of the tuner). Make sure it's set to INPUT so it mutes the input when you activate the tuner.