Not sure if it’s worth mentioning, but I can put my dhw on timer, comes on approx 6am, goes off at 7:45am, will probably last until early to mid afternoon (nobody using it much then). During this timed period, I’ll hear the boiler fire up at least 3 times, is that normal?
how many people in your house? Showers or baths?
using the timer should mean the HW is only heated when the timer tells it to - so if it’s doing HW when the timer is “off” then I’d say you’ve got a wiring issue