From what I understand, it wasn't [Projection] what caused Shirou's pigmentation change in his hair nor skin. Instead, it was [Reinforcement], one of his three basic magecrafts, which enhances all the aspect of an object. Because he was constantly in a warzone, he had to abuse of this power so he could survive and save others.
I'm not very sure of the process myself, but as you can see in the case of Shirou from the Miyuverse, he didn't necessarily know about the projection magecraft, only reinforcement. And to keep up with the attacks of Angelica with the powers of Gilgamesh, he had to abuse in a great extent of his [Reinforcement] on his own body. This version of Shirou can be considered the one who had reached an advance level on this magecraft during an early age in comparison with the other versions.