So, there are hardware in phone whos job is to recognize trigger words and phrases like "Hello Google" , "Alexa" and "Siri" and wake up the phone so it can listen to the users request. They probably have limited memory, but I would not be surprised if they can store a few hundred low quality rules for detecting certain words. The ad-network already have a profile on you, and could compile a list of trigger words you are likely to use based on your profile. They upload this list to the phone, and lets the phone build up a frequency list that they can use to better target you with ads you are likely to click on.

All this would just require a few thousand bytes transferred between the phone and the ad-network. Since they are using information they already have about you, and there are little or no additional CPU or network usage it would be really hard to detect.