colouring knot diagram and its mirror by the same colouring

Question

Let $K$ be a knot diagram coloured by any quandle $X$. Let the colouring used be $C$. Reverse the orientation of $K$ to obtain the reverse of $K$, denoted by $-K$. Then is it possible to colour $-K$ by the same colouring $C$ we used for $K$. I am confused because of the following: suppose we have a crossing point in $K$. Assume the under arc which is behind the over arc with respect to the normal vector of the over arc ic coloured by $x \in X $ and the over arc is coloured by $y$. Then the colour of the under arc that is in front of the over arc is $x*y=z$. Now consider the diagram $-K$ and suppose the colouring $C$ is still valid to colour $-K$. This gives that $z*y=x$. I wonder if this is always the case.