Replaced AC compressor now radiator fan turns on before engine warms up

I just replace a new AC compressor and AC condenser. Everything works properly with no AC leak. My concern is that after I install the new parts, the radiator fan automatically comes on right when I start the motor in cold temperature. I am not sure if that is normal or if I have to of the connectors from the AC condenser backwards (see picture). I always think that fan should automatically engage when the motor reaches to its high temperature and when the thermostats open. Another concern as well. I am not sure where this part connects to (see picture)? Is that suppose to be attached to a radiator or AC condenser and if so which location of the radiator or AC condenser?