A Time Proportional & Integral (TPI) room thermostat measures the room temperature and calculates the difference between the actual room temperature and the set room temperature, in order to work out how long the boiler needs to be fired. This is based on the information it has 'learned' previously from heating your property, and it means that the boiler is fired for just long enough to reach and maintain, but not overshoot the set temperature. Thus saving some energy. That's the theory of how it works, but how it relates specifically to the "3 times an hour" for an oil boiler, I don't know, but Dan's knows his stuff so I personally would go with it.
I seem to remember that the 'set back' feature allows you to drop (or raise) the set temperature for a chosen time period, I believe in multiples of one hour. You set a time period e.g. 2 hours and the temperature you would like it to be for that period. After the 2 hours has elapsed it will go back to the previous setting.
Because you have a Horstmann programmer that will still have overall time control for the heating on & off as it does now. So, if that switches the heating off during the thermostats set timed period, the heating will still go off.