Hello again, Billy is correct ! if the smoke detector goes off when the furnace is in the heating mode and you break the the red thermostat wire. the gas valve and the fan relay will go off,,, but the fan will keep running on its timer or furnace fan control intended to run the fan until the furnace cools down.
You will have to run line 1 from the 110v supply to the furnace through your smoke detector contacts in order to shut the fan off instantly'
Picking up the 24v to run the smoke detector from the furnace 24v transformer
regarding the positive and negative.... those are direct current voltage terms,
AC , alternating current is supplied by the utility the furnace transformer
not DC power'
however with components coming from china lately many items are marked positive and negative when they are intended for AC use
look on the smoke detector wiring diagram for references to AC power
if ac is OK... then the red wire coming off the transformer to the thermostat marks
'positive'.. the other terminal will be called 'negative' even though its AC and there is no actual positive or negative
its a bit trickier than that but no need confuse the issue more than it is
verify the voltage spec on the detector is marked as AC
let me know
we can go from there