Your Rh line is Heating, RC is for Cooling , R is similar but systems might be separated and use dedicated lines.
What it sounds like is that you are hooking up your thermostat for the first time ??
Either your wiring is incorrect or there is a program mode where the fan runs. Since your question says HVAC - I am assuming AC .. however if the Unit is calling for heat Rh .. your system will have a cool down period - the Blower will run after the elements have turned off for about 5 to 10 minutes I think.
A typical color coding of wires is this : BUT DON'T BE FOOLED - Not everyone installs things correctly ..
So, this is what you might expect to see in terms of colored wires and what they mean:
White – The white wire is what connects to the (auxiliary) heat on your system.
Yellow – The yellow wire connects to your compressor.
Green – The green wire connects to the fan.
Orange – This wire connects to your heat pump (if you have one).
Red – Now, there can be two separate wires for this.
One is for cool and the other is for heat,
hence the abbreviation “RH” and “RC”.
Blue – This is your common or “C” wire.
So it would be nice to see a picture of your connections in the NEST and at the Air Handler.
Your wiring seems to be incorrect. especially when there is a message about Rh and you are trying to cool.
Look Here http://www.thermostatcenter.com/thermostat-wiring/
Also Here :
On a thermostat, are "R" and "Rh" terminals the same thing?