Earlier quoted context omitted.
They literally said it's launching in the Google Assistant (i.e. running on phones) now. In fact that's the title of the article.
Does TTS run on the phone or the cloud?
Edit: I might be wrong, at the end of a paragraph they say it runs on Google’s TPU cloud infrastructure, though it isn't clear to me whether they just use that for training.
Edit 2: I just tried it on my phone. At least stuff like asking it to "Turn on WiFi" works without an internet connection, and yields a TTS response.