The fan on the ac unit is turning. But is it turning because the motor is on, or is the fan turning because the air is being pulled through the duct to replace the air that the air exchanger is pushing to outside?

I would say most definitely the motor is on as you can hear it going from quite a distance. I will test that theory when I turn off the breaker tonight.

I'm not real clear on this yet. Is the AC fan turning the one in the outdoor unit?
I've not seen an AC motor inside.
If it is the outdoor unit, is it just the fan coming on or is it the fan and the compressor?

The outdoor a/c unit's fan is turning on when I turn on my air exchanger (With the thermostat set to off) but the compressor is not turning on so the air circulating in my house is room temerature.

If you ac is covered in the winter you should be able to just flip The breaker to the ac (should be independant) and the fan will not run. I know this is kind of putting a bandaid on a bullet wound but it should work as a temporary fix if all else fails.
But believe me when I say I am no expert lol

there is no conection between the outside AC fan motor and an air duct, the outside AC fan is just to cool the condensing unit.

I would get a real HRV guy and bite the bullet for a few bucks and get it fixed properly. this should not be comming on and a AC unit fan is not a cheep one to run. Also you are using the aire exchange in the summer that fan will be running twice as much and I imagin replacing that fan will be a lot more expensive than getting the aire exchange hooked up properly.

Steve

I didn't know we were talking about the outside fan motor. I thought the fan was on the inside of the house, blowing through the evaproator

Well no luck. No matter if the thermostat is set to off, hot or cold as soon as I turn on the air exchanger, the outside a/c fan comes on. Now to decide whether I bite the bullet and pay an arm and a leg to fix it now (As you know they will overcharge me somehow) or just turn off the A/C in winter.

You should be able to trace the wiring from the AC and from the air exchanger to where they interconnect and fix the problem there.

call a reputable company then because not all heating and AC companies are crooks

my companies AC service call is $135 and $95 an hour after

if you dont wanna pay a company your going to have to learn to do it yourself