On subs, since they really can't see outside so most sub operators around the world changes the color of the light to express the time of day. Night time is red and day time is white light.
The reason why they change the color in CIC on a surface ship and on a submarine is quite different.
You don't have to worry about light pouring out from a sub.
For subs it more about adjusting the biological clock of the crew. Without it the people on the sub will start showing symptoms of insomnia which affects overall efficiency.
When you say "don't have to worry about light pouring out from a sub," are you suggesting that on a surface ship, they have dimly lit CICs because they're afraid the light will somehow escape from a window outside and give away the position of the ship? That seems a bit too fantastical, let alone the fact that CICs are often in the enclosed belly of the ship and fairly well protected, without windows/portholes to the outside.
From my understanding, the dim light in CICs in general (regardless of whether it is in a surface ship or submarine) is due to reducing ambient light in the CIC to reduce eyestrain and allow individuals to work better. We see this in other types of rooms with many large screens as well, such as control rooms for large tv stations.
I'm not sure if submarines alternate between bright lights and dim lights during standard "work days," and if that is intended to affect the crew's biological clocks -- if so, then this is the first time I've heard of it as a prime reason.
....doing a bit of searching, I think the the red light use in submarines is more associated with preserving night vision, eyestrain and transitioning to mission ready status (near complete dark) than biological clock related, per se -- after all, crew on submarines tend to do six hours on, six hours off (or a variant of that work schedule), so their biological clock during missions would be completely changed from being on land on the surface anyway.
In a surface ship's CIC I think it is more consistently dark, so red lights may be less needed. That said, some CICs have also been photographed with red lights but they seem to be more of a feature for submarines.
.... Also, funnily enough (at least in older submarines), there seemed to be a risk of light emerging from a submarine's periscope that could be detectable by surface ships -- if the interior of the submarine was well light the periscope would naturally reflect that light outside, which is why submarines with older periscopes operated with dark interiors during missions... so in a way, there is a greater risk of light "pouring out" from a submarine's operations room/CIC (with older periscopes) to the outside, than there is from a surface ship's CIC!