In that case you'll need to write to all the major manufacturers and get them to correct their manuals!
The maths is very simple.
If you have a 3mm leadscrew (like the example in hand), and you want to cut imperial, you need to speed up the leadscrew slightly. The simplest example would be to cut an 8tpi thread which has a 25.4 / 8 mm pitch ie 3.175mm. So for that you drive the 120t gear and the 127t gear drives the 3mm leadscrew gear. This gives you the correct ratio, as 127 / 120 x 3 = 3.175.
Going the other way, if you have an 8tpi leadscrew (3.175mm again) and require a 3mm thread, you need to slow down the leadscrew by that ratio. So you drive the 127t and the 120t will drive the leadscrew gear.
It's really not rocket science.
Murray