Simple - flip the "dir" pin on your Z axis to "active low" (or if it on active low, then "unflip" it)
The Z axis should be negative going down and positive going up.
I have no doubt the vendor made the correct connections etc for your mill, but Mach 3 has a lot of configuration still for you to do. You should also check - althougn it appears you have - that your other axis are going it the right direction. This is one of the fundamentals, and a lot of other stuff follows on - i.e. jogging, homing, etc.
Look in Config/Port and Pins.