I have no experience with those Chinese controllers but I'm sure you could find on google the info you need. I think your only problem is assigning in mach3 the corresponding port and pin number for the input you need.

If you suspect something wrong with the controller you could check at least that the input signal goes through the optocoupler.

I don't think there is a problem with using a new mach3 licence with an older version of the software, the one recommended for the controller. Even in trial mode mach3 has full functionality except for limiting the g-code to 500 lines.