On the Mini 9, the port closest to the power connector is a "full powered" port - the others are rather lower powered. There's nothing in the manual about this. I am surprised that the right-hand port is the one that works for you - that's not what I would expect. Other than the power issue, all the ports really should act the same, but I have seen cases with various PCs where they don't.
One thing that can be a problem is that Windows recognizes combinations of devices and ports - it will remember device X plugged into port A, but the same device plugged into port B is treated as something new. So perhaps it is an issue where Windows "remembered" bad information about the tuner in the other ports.
Offhand, I'm not sure how to resolve this except, perhaps.. Plug the tuner into a "bad" port. When it comes up in device manager, select the option to uninstall the device manager. Remove and reinsert the device.