JohnW wrote:
The furnace appears to be made by International Comfort Products
Corporation and is the NTG3/FBF model (at least the serial number
have NTG3 as a prefix). The manuals says Installation 80+ Single
Stage.

Just as a matter of historical interest, Carrier (United Technologies) bought
ICP in 1999.

The programmable thermostat has only one set of terminals, but the
inside of the terminals are coded for conventional lettering, and the
outside are coded for heat pumps, but share the same hole for the
wi

Heat Pump Conventional
C C
G G*
Y Y*
O/B W*
RC RC
R R*

The asterisks indicate which wires I've connected. Also, the RC and
R are jumpered per instructions.

A second post has:

Conv. Heat Pump
W2 Aux
Y2 E
L
but nothing is connected there.

W2/Aux is where you'd connect the 2nd stage heat (if you had a wire for it).

I'll just see how fast I can get service in here to explain exactly
what we have, what to expect, and confirm the programmable is set up
correctly.

It sounds like you are set up OK and that the outdoor thermostat is
determining whether the HP or propane funance is used when the thermostat
calls for heat. How is the system working today?