Consider these two phrases:
“They've raised their hand”
“They've raised their hands”
Does object have to agree with subject? To make the question more clear, let's assume all of them have raised their right hand/hands(?). Now we have five people and five raised hands.
I've changed the original question which used idiom "to show one's true colors" as example, which was giving the idea that my question was about usage of the specified idiom. I apologize for my poor choice of example.