Maybe local text-to-speech is not plausible given the heavy processing and battery drain. What if instead there is a list of words/brands being listened for; my phone is always listening for "OK, Google."
All I know is that things that I have talked about with my phone around 1-2 days prior, I suddenly see ads for. Things I did not Google or mention on the Internet. In one case I started seeing ads on Instagram for a product that I posted a photo of and did not even include the product's name in the post. Dishwashing liquid that I would never even buy (I'm not the target user so it wasn't target marketing).
It's all a little too much for me to believe it's a coincidence.