My water pump turns on when wall thermostat calls for heat. Set up via relay. When I installed outdoor boiler, I too was concerned anout cold air from water pump lag time, but reality is, convection currents always keeps warm water in the heat exchanger. My unit never blows cold air, even if thermostat hasn't called for heat in a while.
I think many are set up to run continuous when hot water heat exchanger is on the same line as the furnace heat exchanger. My heat exchangers are on seperate lines / pumps.
Either way works fine.