Yeah, my first CNC Lathe +30 years ago was a Mazak QT8 with tool setter arm.
I asked, because I am pretty sure auto measure on rear mount configuration has a bug anyway.
I would prefer not to use the reference tool solution on a lathe, but a fix XZ zero for the machine coordinate system in front of the chuck and two parameters for the XZ center of the tool setter, for its XZ size there are already parameters in use now. In this case with two more parameters for the XZ location of the turret tool holder mounting surface, tools could be measured outside the lathe too.
The cream would be a full integrated Y axis
But the reference tool configuration can work with off center tool setter also if the internal calculation is done right.
Uwe