3 Colorability reduction to SAT
With your modeling, setting $i$, $i_r$, $i_g$ and $i_b$ to false for all vertices yields a solution of the SAT problem and this is not a solution of the graph coloring problem.

You need to add clauses to say that each vertex is blue or green or red, namely
$(i_r\vee i_g\vee i_b)$.
Then it becomes a 3-SAT problem.

Note that if a vertex is assigned to more then one color, then we can take any of its colors and obtain a 3-coloring.