Question on how to use HVAC with damper

We just moved into a house that uses a damper to regulate the heat and AC. The upstairs thermostat can turn on the AC, however the downstairs thermostat only turns on the fan. If the upstairs has AC blowing, we can go downstairs and adjust the temperature on the downstairs thermostat and cause the damper to allow the AC to blow downstairs. Is this normal?
How does one correctly use a system like this?
Many thanks in advance!