The default configuration is cloud based. However you do get to choose where your voice data goes. They also have a method to keep the TTS local and I haven't checked in on the project in a while but they were either working on or already had a local home server so you can make the whole system internal if you wish. I'd provide reference links but as noted site is down currently.

Edit: There are also several skills available that can point at full, local, downloads of wikipedia and the like. So if you prefer faster results and keeping some of your queries internal as a sort of hybrid thing that's an option as well.