The DAB antenna amplifier is not under the headlining, it is under the hard plastic trim section at the top of the rear tailgate.
There is a thin plastic drainage tube connected under the rear badge, this can be seen at the bottom of the hatch when you open it.
This tube locating rubber often rots or becomes dislodged, which means water does not drain out on to the top of the rear bumper as it should.
As it is not draining out of the tube, water collects in the bottom of the tailgate, then, when you open the tailgate to the upright position, water runs down inside the tailagte on to the electrical components sitting at the top of the tailgate, one of these being the DAB antenna.
Make sure your drainage tube is there and in working order, or it may well happen again?
I purchased a new tube for around £8 from VW, you do have to remove the rear tailgate trim to fit it.