Think of the ecobee as a programmable switch with 'dry' relay contacts (this is one reason why it is perfectly suitable for this application). When the ecobee calls for 2nd stage (emergency) heat (propane furnace), the ecobee internal relay for W2 makes contact and sends +12v to the W2 lead. All you are doing is basically adding another 'switch' across W2 to provide +12v.
That reminds me, you need a really, really simple thermostat exactly like the one used for the vent fan and the rear furnace, otherwise you will need to tinker with the guts of the typical AC/heat thermostat like you would find in a hardware store.