If thats truely melted plastic then more likely is you had a partial short and the 19V was dumping bursts of high current between the rings and slowly heated it. The question is what got between the two rings that made the partial short. Was there any organic or conductive stuff between the rings that you removed?

When the mug is on the base do you get a power indicator to tell you its working?

I dont think its a fire hazard but its certainly suspect. Gouge out the burnt plastic and see if there is a PCB hiding under the surface that those two gold rings are part of.