Anecdotally, the only times I've ever noticed these chimes and the auto-braking (even automatic rolling-up of windows), it was false positives, and it was mildly terrifying: for a brief and unexpected moment I was no longer in control of my vehicle. [Recent Honda Civic and Audi A3 models]
I've only had a couple weeks in rentals with automatic emergency braking, and was very nearly been rear-ended twice due to false positives. Anecdotal, and I'm sure they'll improve with time, but I would never allow the system I experienced anywhere near a car I owned. It was profoundly unsafe.