As I sometimes do, I will add My 2 cents without knowing all I should. The area of the parent metal that excedes the allowed temperature does not extend real far from the cut, and does not stay at that temperature long. Some of this material will be ground off, some more will be melted in with the rod and alloyed to give more ductility and better grain structure.
As mentioned, close to the edge of the puddle [in the HAZ] the part will excede maximum interpass temperature as well, but that is not where You are instructed to measure it.
Time at elevated temperature is what You are keeping under control by following the max interpass restrictions.