There is an incorrect setting in Human Playback Preferences which prevents Jazz KS mutes from working in Finale 2010-2014.5. To correct this, follow these steps:

  1. Open a document that uses the JABB 3 library.
  2. From the MIDI/Audio menu, go to Human Playback, and click Human Playback Preferences.
  3. Expand the Garritan: Jazz, Big Band & Marching Band category under Instrument Techniques and Effects.
  4. Double click the Brass: Cup Mute technique.
  5. Under the Apply Only section, keep the filter as is, but change the text in the text field to "Garritan" (without quotes).
  6. Repeat steps 4 and 5 for the remaining two mute techniques.
  7. Click Save and Close.

The mute key switches should now trigger properly.