Exactly! Not sure why they designed and produced the stat like that!The divisions on the cylinder stat are extraordinary at 6.66C/division just to create more of a challenge when setting it?.
Anyway, to test the stat, just turn it down and see if the HW cylinder zone valve closes while programmed on.
Your solution to test the stat proved right! A few months ago, the very first time when we found the boiler was still firing even the programmer was off, the zone valve for hot water was opened, by chance, we turned the stat of the cylinder smaller, and saw the zone valve closed and boiler stopped, so at the time we could see the stat temperature setting seems working.
(then next time when it happened again: zone valve for hot water opened & boiler fired outside of programmer setting period, even if we turned the stat of cylinder smaller, boiler still continued to fire, so second time maybe zone valve issue.)