Hello, I’m Paolo from “Le Piantagioni del Caffè” and in this video I’ll tell you what is the
correct position of coffee cups on the espresso machine.

The correct position is the one you see here on the right. That is with the base facing the coffee machine. Because the coffee ends up on the bottom, this is precisely the portion of the cup that must be hot in order to avoid a sudden temperature drop of the liquid.
If the cup were placed in the opposite position, one could burn her lips when approaching the cup to drink plus affecting the taste of coffee too.