IAS is derived from the dynamic pressure of the airflow at the inlet to the pitot probe. The dynamic pressure (1/2Rho V squared) is proportional to the true airspeed. The greater the dynamic pressure, the greater will be the airspeed indication.
If an aircraft in flight experiences a sudden tailwind, the inertia of the aircraft will tend to keep its ground speed constant. But the tailwind represents a sudden decrease in the speed of the air relative to the pitot probe. So the pitot probe and airspeed indicator sense a lower value of dynamic pressure. The airspeed indicator therefore indicates a lower IAS.
But the greater problem is the fact that the wings also sense this reduced dynamic pressure. This reduces lift thereby causing the aircraft to sink.
The reduced dynamic pressure also reduces drag. So if the tailwind persists for long enough the aircraft will eventually accelerate until its original IAS is restored, but at a greater ground speed.
So sudden (brief) tailwinds do not affect ground speed, but reduce IAS and increase ROD. Prolonged tailwinds (eventually) increase ground speed.