We had encountered the issue of false trigger with the Ubi back in 2013 and had to spend some time working on solutions. The Echo and Google Home, and many DSPs being used for Alexa Built-In and Embedded Google Assistant use several algorithms together to help clean up voice audio. These include active gain control, beam forming, blind source separation, and acoustic echo cancellation. The latter is like ANC.
Beyond cleaning up the audio signal, you can also dynamically change the acceptance confidence based on noise or voice activity detection. Other strategies include updating the model with a better trained one (you can run larger models on an application processor vs a DSP target) or swapping out to a new wake word detection method altogether (interchanging Sensory, Kitt.AI, Porcupine, etc).
Amazon (and Google) also have cloud verification of the wake word. Essentially, they cache the audio being recorded, including the wake word, and then ship it to an engine that verifies the wake word was spoken if the device is triggered locally. If it’s determined it wasn’t, it shuts down the audio stream. Interestingly, there seems to be a slight delay now in the Echo LED indicator upon speaking the wake word, perhaps to mask false trigger.
In the end, false trigger (false acceptance) is much less of an annoyance than false rejection and any local wake word is walking a tightrope between these two scenarios.