I don't frequent this forum much, is your problem now sorted as it was listed a while ago (but no one else seems to have chipped in).
I need to understand what the proma is doing?
You say "when I started to cut something, Z axis goest straight to THC min value".
Presume, you do a touch off (zero the Z), back off to the pierce height, fire the torch, wait for the ARC OK from the Proma, then wait for the pierce delay, drop to cut height, then begin motion, then after a set time you turn on your THC once the voltage has stabalised....
Note.... the proma is not very quick to respond as it uses relays internally (contacts that take a while to make + break).
What you may find is because you are now using a negative value to Zmin, the torch is diving below the 0 Z-axis position because the proma is telling it to THCDN because the voltage setting is too low and the THC voltage being sensed is too high (relative to the setpoint).
Where as with your old screenset (where you could not lower the Zmin below zero) the torch (Zaxis) was only able to dive to zero and then Mach3 ignored it's motion any lower than this.
There are only a few settings within the Proma.
One of which is the transfer voltage.... when I was using a proma, I set this voltage lower than the transfer voltage (I actually set it at about 120V when my target voltage was about 90 / 95v)
Also the hysterysis is only about 1 or 2 volts minimum, hence I set this fairly low / close.
What you find is if you have a fast Z it may shunt your Z up and down and crash the torch (because it's only bang-bang control [UP / DN / STOP]) hence you end up having to counteract this by slowing the Z-axis velocity setting.
Note mach3 (and most CNC software) ignores the Z-axis acceleration when making THC movements and it will just shunt it up and down at the maximum velocity / THC speed setting.
Suggestion..... try running the cut without THC on a relativly flat peice of steel and view the voltage on the proma (is it telling your machine to dive?) If so, move the voltage setpoint up a bit and try again.
Also what plasma cutter are you using? The Hypertherms have good manuals which list the cut and pierce heights and feedrates for various materials and thicknesses.... all the other seem to be guesswork...