TPMS warning will tell when a tire is low and it will tell if a tire has too high pressure too. When the pressure of any tire differs 7 psi or more from the other tires the light will come on. You need to also know that the TPMS monitors are battery powered and those lithium batteries last 5-12 years, so the early ones are starting to die. The batteries are sealed into the monitor to make you not try to replace them. They are soldered to their circuit. Tire shops will not try to excavate the battery to be unsoldered and replaced, so you buy a new monitor instead after the old one's battery dies - or just ignore the light.
Oh, your question; Several answered you. They monitor pressure, not material. It will take time after the nail pierces the tire, for pressure to go down enough to trigger the light.
Some cars need the system reset after tires are rotated since they indicate tire faults by position. Some manufacturers (Ford) use a $35 clicker to do that reset. Sometimes Toyotas will get stuck in a reset loop and need the TPMS to be rebooted with the $50 Bartek tool. When you replace TMPS monitors ($50-$80 each), those need to be programmed to the car with a very expensive computer. If everything you try by the owner's manual fails to turn the light off, go to a tire shop, such as Firestone or Big O to have the TPMS system analysed. They can tell if any sensor is weak or failed, without dismounting the tire.
Maybe all you need is to have the tire patched. I got that done at a used tire shop for $15. Passenger car tires should never be inflated to 50 psi. See your tire pressure label in the door jamb, for your correct pressure.