Is my Heat pump and gas furnace installation incorrect?
The tech made it sound worse than it is. It's not in the wrong air flow, just the wrong order, so moving the pipe will not help. It's a fair sized duct, not a pipe.

There is a restriction in at least the International Mechanical Code about heat exchanger coils being before the furnace. It is because in cooling mode, the resulting condensate can be corrosive. In heating mode the physics involved are not really a problem, but that doesn't change the code.

There is an exception to this requirement, it is OK to configure the system this way if the appliances are listed for such configuration. You would need to obtain the installation instructions and see if this is indicated as an option.

The only practical way to fix this if you cannot prove the current configuration is allowable is to relocate the heat pump coils upstream of the furnace.

Note that the direction of airflow is the criteria for placement, not above or below.