I can’t find a requirement to connect the primary drain to the sewer line but this is the first time I’ve seen a double pan scenario like this.
There was an identical unit like this one at the rear of the attic space where the primary was connected to the plumbing drainage system.
I would of thought that they would have just plumbed the primary to the outside. Any ideas why they went to the trouble of installing two pans?
You’ve got stains in the second pan as well.
I’ll bet they just added another pan (underneath) to catch what was coming out of the top pan.
Cheap fix.
Do those cool clear hose sections allow inspection for impurities in the discharge? 
I have see this before but I never got an answer for your question.
Just that it is wrong! Yes, trap and run a drain as you said.
**M1411.3 Condensate disposal.
**Condensate from all cooling coils or evaporators shall be conveyed from the drain pan outlet to an approved place of disposal. Condensate shall not
discharge into a street, alley or other areas so as to cause a nuisance.
**M1411.3.1 Auxiliary and secondary drain systems.
**In addition to the requirements of Section M1411.3, a secondary drain or auxiliary drain pan shall be required for each cooling or evaporator coil where damage to any building components will occur as a result of overflow from the equipment drain pan or stoppage in the condensate drain piping. Drain piping shall be a minimum of 3/4-inch (19.1 mm) nominal pipe size. One of the following methods shall be used: