I am pretty certain that this is a issue of in which order you connect/start things. Please check out the following thread (it’s for the Play+ but it works exactly the same for the Mini):
The essentials:
Disconnect everything and turn off the Mini
Do not start any app on the iPad yet (close them if you still have them open)
Connect the Mini to your iPad
Turn the Mini on
Then start your app
This should resolve any distorted sounds you may get. Let us know if this helps
