They rolled out the app last Fall and I knew that if you had been in close contact with other covid-positive persons with the app for an accumulated 15 minutes it would alert, and I also knew that if you had been to a cafe or restaurant or pub that later recorded a positive case then you would get alerted, but that relies on the fact that you check into each place by opening the app and pointing your phone at the QR code outside each place you are going to enter. (The greeter always checks that you have done this, or gets you to physically sign in)
It is a small step to surmise that when a business has a positive Covid test recorded against it their premises are tagged, such that when an individual has had a positive Covid test and is told to isolate at home that their home is tagged as a Covid hotspot. I have just checked my NHS app and it does not use location settings, unlike many other apps, and states specifically that it will not track locations and all data is stored anonymously.
I now think the engineer misunderstood or misremembered the phone call, and that someone in the household also had the app on a phone and that is what triggered the alert. I've talked to others, such as my sister, who have tested positive and the moment they enter the positive test unique code they are sent then the phones of their family members in their house immediately alert them.