It has constantly the value to show 1/10th during all operation time, also after 12 sec.
Are you refering to the point that within 12 sec you can read the full and the 1/10th sec with the red hand only?
Than the regular rhodinated, central second hand would have no use, within first 12 sec.
In my view the red hand is only showing "perpetually" and "independantky" 1/10th, all all time and circumstance.
Regarding independancy:
This is why I said in brackets (Patek is saying that).
To me too it is also not an indpendantly running chrono, as you said, they would need to be activated independantly to be so.
I think Patek refers to the "independant" display and measurement from the center, as both hands are running very differently together in the center of he dial.
Best
Moritz