Hi , the stat will turn the boiler off as soon as it has reached the set temperature.
it should be correct .the difficult thing is the water is hotter at the top of the cylinder and so positioning of the stat is vital
The determining factor though is where the stat is positioned and the size of the cylinder.
Sometimes there has to be a repositioning.
The stat should be set at one third up from the bottom. The foam insulation should be removed and scraped off clean so the stat is sitting on the copper/steel tank .The ideal temperature to set it at should be 62 degrees. Over 60 kills legionaires , but scale forms at 65 so arou d 62 is best.