Re: Furnance came on
One of your thermostats controls the furnace as well as one air conditioner. Some thermostats, the Dometic Comfort Control II for example, have an auto mode that's supposed to switch between air conditioner and furnace automatically. This is different from having the FAN Mode set to AUTO. If the temp at that thermostat dropped by a few degrees, it might have shifted into heat mode.
If you'd like to control what happens, change the thermostat mode to either COOL or HEAT and it will operate in that mode only. Keep the FAN Mode set to AUTO. If the fan is set to high or low, when the furnace starts, the A/C blower will also start, pushing air out the ceiling vents.