First thing that comes to mind is there too much return in the lower level and not enough for the upper level.
Sounds like they took the fast , easy and cheap route of calculating the distribution system and not considering all the variables to give you a properly designed sytem.
Chances are they used the square footage of each level and simply installed supplies and returns based soley on that. When in fact you may only need half of the return volume in the lower level based on the layout of the lower space , amount of conditioning , etc..
If your air delivery system ( or air handler ) is a constant volume single speed blower then it's a mater of ensuring properly balanced supply and return are in place based on the variables for each zone. Along with ensuring that static pressure is not affected by the state of each zone-- upsetting the balance.
With a variable speed blower it can be somewhat easier to regulate the air flow for zoned systems --- but ---- the supply and return still need to be balanced.
So , what's needed to correct your issue ?
It's time you called another HVAC professional who is knowledgeable with zoning forced air sytems to evaluate yor situation and come up with recommendations.
It may be redoing the supplies and return to properly balance the system.
Whether it's more of both in the upper level and less in the lower level or even a bypass to relieve static pressures it's hard to say sight unseen.
It"s not rocket science for HVAC professionals who know what they are doing to install a zoned system --- just some careful thought and planning.
2 cents worth.