The product criterion for Type-2 isomorphic circulant graphs

Let $C_{n_1}(R_1)$ and $C_{n_2}(R_2)$ be circulant graphs such that

$$C_{n_1}(R_1)\Box C_{n_2}(R_2)=C_{n_1n_2}(R)$$

for some $R$. Product criterion conjecture. The graph $C_{n_1n_2}(R)$ has Type-2 isomorphic circulant graphs if and only if at least one of $C_{n_1}(R_1)$ and $C_{n_2}(R_2)$ has Type-2 isomorphic circulant graphs. This conjecture is proposed as a consequence of problems 3.1, 3.3, 4.1, and 4.3; its resolution is not specified in the source.