why the rate of descend is smaller in tailwind on a power idle descend
It is not smaller,rate of descent is unchanged with either HW or TW.
Rate of descent is dependent on thrust,drag,speed schedule and weight.
However, flight path angle is increased with a HW and decreased with a Tailwind and ground distance from T/D is increased in a tailwind and decreased with a headwind.
If you find in the FCTM a table for Rate of descent changes based on HW or TW ill buy you a couple of Tsingtao