does it mean that the track officials are responsible for plugging in the blankets ?
No, I don't think so. It just means that the car had time to cool before the measurement was taken. I don't know what the measurement procedures are or when they are done.
The driver is weighed in immediately after the race. The car is too at some point.
The issue arose late in the race so I suspect that the tire pressures are measured before the race starts or they rely on telemetry (though that couldn't work during the race since the tires heat and cool drastically between corners and straights).
What I am astonished by is that they pull 4 to 4.5 gs on the corners and on one corner at Monza 5.8 gs of deceleration! This is with the slower cars they are running now.