Air Handler with no condensation
Yes, the second level unit is most likely gravity drained and the first level unit needs the ejector pump.

The ejector pump is used to pump condensate water to a higher level. It only operates for a minute or so when there is enough condensate water in the container to trigger the controls. It is not a continuous thing.

However, there will only be condensate when the humidity is high enough to collect on the evaporator. So, you need high humidity and a cold surface on the evaporator to collect condensate. This only happens while running the air conditioning.

So, depending on where you live (they call it the desert southwest for a reason) you could have very low humidity. In that case the condensate could evaporate quickly or never form at all.

Additionally, heat rises and the second level unit could be removing most of the humidity. Leaving the air too dry for the lower unit to collect any condensate.

Finally, as long as water is not collecting in the wrong place, leaking or damaging something, the units are operating normally. Don't worry about it.

Happy Day!