There are a few options for DIY stand alone controllers that can synchronize audio with servo control (that I am aware of). None of these are off the shelf easy to use but are free and open sourced…
1) Falcon Player – If you create your sequence in Vixen or xLights (both are Xmas lighting sequencing software) you can export the file and run it on a Raspberry Pi running Falcon Player (FPP). This will give you a stand alone controller. If you already have sequences created in VSA you can import them into xLights and then export into a file that Falcon Player can use. FPP/Vixen/xLights are very well supported for lighting control but not so much for animatronics.
2) Lightman’s Servo Controller – This is a Parallax Propeller based 8 channel servo controller. Once you have you audio file loaded you sequence the servo movements via attached pots in realtime in a record mode. You can then play the various sequences syncronized with the audio.
3) Bechele2 – This is a Raspberry Pi based 16 channel servo controller. Again it has a record mode to get the servo motion from an attached joystick and then you can use a player mode to play your sequences with the audio.
I have more information about these and other animatronic controllers on my Animatronic Control page: Animatronic Control Systems