Not sure about your setup but the circulator/timer on mine is for making sure it doesn't go out or doesn't overheat. There's an additional setting for high and low.
The timer runs the furnace for a few minute each hour/ half hour etc. year round to insure that it doesn't go out. It's not really needed in the winter as there is plenty demand for heat. We run ours year round to heat the hot water before it goes into the hot water heater and because it's cheaper to keep it running that the repair bills you will incur by allowing it to go out. the larger furnaces are meant to run constantly. In the summer time the timer runs every hour since it wouldn't run otherwise.
The circulator will run the water when it reaches a certain temp. Ours is set up very high, around 220 degrees or better I think. This will run the water through the baseboard regardless of whether there is demand for heat or not, it's a stopgap so it doesn't overheat. Other wise the emergency relief valve would eventually go off which isn't really a big deal but it is something to be avoided if possible.
There's also a high and low setting, in the winter the high is set at 180 degrees. The furnace will run until it hits this temperature, once it does it will turn off but the water pumps will continue to run. It won't start again until the temp drops below 180 providing there is a demand for heat. The low is set at 140, any time the temp of the water gets to 140 it will run until 140 is achieved. This is rare since it never goes that low in the winter, the only time that kicks in is in the summer and that's not very often.
Do you have a thermostat hooked to your furnace? If you do I'd suggest that is your problem, that's what really controls whether or not it pumps heat.