So far as I'm aware there is no good description in the literature concerning the how's and whys of metric threading dial operation. Due to metric threads being rationalised by pitch, rather than turns per unit, and the associated lack of common factors the whole idea seems to be considered something of a mechanical malpractice. Most descriptions cover the simpler, inch, case and tack on the metric version as a confusing aftertaste. Lets take a run at it anyway and start at the beginning.
If the lead screw be stationary running the carriage back and forth lets it act as a rack driving the dial via its gear. For any given lead screw pitch and number of teeth on drive gear the carriage will move a specific distance. In principle the dial can be calibrated in terms of distance moved per turn or fraction there-of. Although not explicitly stated this is what is done in the imperial case. This idea is generally considered impractical in the usual metric set up which uses one dial and several gears to cover the various pitches.
If the carriage be stationary and the lead screw turning the screw acts as a worm driving the dial round via its gear so the dial graduations acts as lead screw (and spindle) turns counters. Its the mutual integration of carriage movement and screw/spindle rotation indicated by the dial that lets you select the right place to close the half nut so that successive threading cuts are in sync.
The normal metric set-up of interchangeable dial drive gears is a complete pain to explain but there is a system on some Harrison lathes which uses single dial and gear to cover most metric pitches. This set-up uses a 6 mm pitch screw with dial carrying 20 divisions of which four are marked with longer lines and numbered 30, 60, 90, 120. The gearing is such that the dial makes one revolution for every 20 turns of the lead screw when the carriage is stationary. Clearly the dial is actually graduated directly in mm of carriage movement viz. 120 mm per full turn and 6 mm, one lead screw pitch, per sub division.
Where the pitch of the thread being cut is an exact whole number sub multiple of the lead screw pitch the nut may be engaged on any line at random without upsetting thread synchronisation. This works for 0.5, 0.75, 1, 1.5, 2, 3 and 6 mm pitch.
For 1.25, 2.5, 5 and 10 mm pitch the half nuts can be engaged on any numbered line. In this case the pitches are exact whole number sub multiples of 5 lead screw pitches i.e. 30 mm.
For 4 mm pitch the half nuts can be engaged at either of a diametrically opposite pair of lines i.e. 60 - 120, 30 - 90 (works for unnumbered sub divisions to but .....). This works because 4 mm is an exact sub multiple of 10 lead screw pitches i.e. 20 mm.
I've never really understood why this system isn't more common as it seems to cover a useful range of pitches in a simple manner.
Hopefully that will help you figure out what's actually going on with your lathe. The essential point is that the engagement points need to be an exact factor of the lead screw pitch multiplied by any suitable whole number.
Clive