The typing works if you think of them as Cinderella Girl types rather than ViDaVo. Hokuto being the cool guy and Shouta as passion
In the brief time I was able to play the game, I noticed my starter Teru's highest stat was actually Dance during the boss round with Shiki, so the Red/Blue/Yellow structure isn't necessarily classifying them by best vocalist/dancer/charisma
I was under the impression that the symbols indicated what kind of idol they were. For example, red cards have a fire symbol, so I took it as those under red are the hot-blooded, passionate idols.
But if we split Jupiter up in the categories in ML and CG, I think Touma would be Vocal and Passion, Hokuto would be Visual and Cool, Shouta would be Dance and Cute.