A product you were just talking about pops up in an online ad. How? Advertising algorithms are so good that they may know what you want even before you do. C...
The device wouldn't necessarily have to be constantly streaming the audio to a central server. If it's capable of hearing wake up words like "Ok Google" it's capable of listening for other phrases and having onboard processing to relay back the results much more compressed. Whether or not this is common practice is another matter, and yes the algorithms are scary good even without eavesdropping.