which was in late June 2016 when, according to Montre Exacte, the '
ViertelUhr' watch was only
2 weeks to presentation...

The 'Vierteluhr' (quarter watch) is meant as a homage to the 4 quarters which constitute the brand's homeland of the Austrian province of Lower Austria which is historically divided into four quarters (the “Wine quarter”, of the “Forest quarter”, the “Cider quarter” or of the “Industrial quarter”).
The seconds indication is rather unconventional: instead of a complete 360º revolution each minute, it moves retrogradely only one quarter of the dial scale, i.e. 90º, and then jumps back. At the same time the sub-dial at 3 o'clock also jumps from 12-3, 3-6, 6-9, and 9-12 and so on.
The technical implementation seems to be quite tricky as well as the odds of finding suitable suppliers in Austria. the initial presentation of the ME ViertelUhr was originally scheduled for 2013, I am still waiting...
So, as Phil said, in order to tell the time, to the second, you need to look at the sub-dial, multiply the position the hand is at (0, 1, 2, or 3) by 15, then add on where the second hand is. In the image above, the time is 10:10:17.
If I understand correctly, there are different versions available for all 'quarters', i.e. you have the seconds hand covering a different quarter of the dial.
ME mentioned it produces about 80% of all parts in-house. The watch so far is estimated to cost well below € 5000, which I think is quite a feat given the claims given the standards they want to achieve in terms of finishing.
As for the background, founder Christian Umscheid has a considerable track record of working with Audemars Piguet. He is a particular expert in refinishing AP Royal Oak cases. So if your RO needed special care it is well likely that it passed through Mr Umscheid's hands.
Hope this helps.
Magnus