Did it ever work right or is this a newly implemented project?
There should be check valves to prevent one pump from causing back flow in the other circuit. Sometimes the check valves are in the pump.
Here are some things you can do to aid in the diagnosis:
If the system is new, make sure any check valves and the pumps are installed in the correct direction. If it worked well before, they are probably in the correct direction.
Draw a flow circuit diagram including circulating pumps, all tees and valves, and the boiler. Contemplate that diagram and see if anything jumps out at you. Post it here if you can.
With both circuits cool, turn on the thermostat to cause circulation in the downstairs circuit. Then, using your hand to check temperature, determine if there is flow in the upstairs circuit (pipe will get hot) and direction of flow (which end gets hot first).
Check to make sure that ONLY the downstairs circulator comes on when doing the test above. They are quiet and you will have to look closely or feel the motor to see if it is on.
Post the results of the test.
Now to the valves. They are probably plug valves (miserable things that will become difficult to turn). They can be used to balance flows in systems, or to isolate the circuits.