It's great that you're focused in on privacy but that's not what's happening.
You can examine every byte of traffic off your phone. There isn't an open audio stream: it'd be too obvious. On phone analysis is too computationally intensive to be inobtrusive.
You're experiencing some combination of frequency illusion and priming when you experience these "phone listening in".
It is far more likely that you had seen the product advertised before but not consciously considered it (priming) followed by a discussion which made you more aware of it so you noticed the ads more (frequency bias).
The fact is companies don't even need to record your conversations to know how to get you to buy what they want you to buy.