I recently bought the house, and this is the first time I have had the
unit tuned and cleaned. So, the problems are not due to the company I
called (unless he did something to clog up the secondary).

What I understand is: The primary heat exchanger has rust on it. He
said the AC coils and the Humidifier could contribute to the problem.
The smaller second furnace (same age and type) does not have a
humidifier, and he said the heat exchanger looked good on that one.
Other than that, I have no idea what is causing the rust. The furnaces
are in a nice dry basement. Humidity use to be 50+% in the summer, but
we installed a whole house dehumidifier that keeps it in the 40% range.
If it was a prior humidity problem, I would have expected both furnaces
to be affected equally.

He said soot in the exhaust pipe is a sign of a clogged secondary. My
guess is that exhaust gas from the primary has to bypass the clogged
secondary, and somehow creates a soot problem in the exhaust pipe.
Maybe the soot is suppose to deposit in the secondary and be cleaned
out by the condensate?