My understanding is that multiples of 12 seconds are redundant, nothing of interest.
The central regular, rhodinated second hand counts the seconds as usually, up to 60 seconds, than the minute counter jumps.
The red laquared hand counts at the same time "perpetually" a 1/10th, gedardless of its incomplete or multiple conplete cycles on the dial.
It only takes 12 seconds for it to pass a full cycle, regular second hand shows 12 sec.
From 12 1/10th second onwards on the next 12 sec cycle starts, but only 1/10th are of interest, as the regular second hand shows the second 12 sec cycle anyway, as it is moving beyond 12 sec .
Even more:
regardless of the position of the regular hand the 1/10th is running independantly (this is what Patek is saying).
It is actually a double chronograph, "like" the double split is also a double chrono, but with differnt property:
display of seconds and display of 1/10th of a second at the same time, hence two independant measurements.
I also saw the 1/10th display as a "magnified" display, same as you feel about it.