Um, no. The temperature change seen by the milk is the same, whether you add the tea to the milk or the milk to the tea.
The temperature change seen by the cup, however, is less severe when adding hot tea to cold milk in the cup than when adding hot tea to an empty cup. Which can, in some cases, be enough to make the difference between the cup remaining intact versus undergoing what mobile phone manufacturers term "spontaneous rapid disassembly".
But people like to make up all sorts of stories to kid themselves it's nothing to do with their cheap china .....