I don’t understand how the attic environment is making it’s way into the house. The unit should pull from the returns, through the unit and out the outlets. I don’t see how you would be getting attic smell in the house. It is basically a closed system unless no returns were put in. In that case it would pull air from the basement if that is were the unit is. Is the unit in the attic? I never heard of that being done in the NE before.
Where is the return air routed? IF it is like some homes, it routes using wall space for part of the ducting (which is bad). That could be the source of odor.
If the ducting is all sealed properly (I hope “duct tape” isn’t what you and the contractor have been using it won’t last long even if you were to find the source of the air leak. Mastic is about the best thing to use. Lasts for decades.
But I echo the prior sentiment - the “stale” air is getting sucked into the system - that would require a fairly large air leak (actually, probably multiple large air leaks) in the delivery ducts. I would suspect the return Air (the air going TO the unit).
It is very common for retro0fitted air handlers to be installed laying flat in the attic, with the return just below it (usually in the ceiling of the 2nd floor hallway), while the compressor is installed outside, next to the house. The situation described here sounds like the handler is not getting its air through the return for some reason and is therefore drawing air directly from its surroundings, ie., the attic.
This situation is very unusual and something is definitely not right.