To simply answer the question: No, squirrel aren’t nocturnal animals. Squirrels are the type of animal that work during the day and rest in the night, very much like us humans.

Squirrels enjoy searching for food during the day because they rely on the temperature to search for their food, and searching around at nighttime makes it rather difficult as they have a harder time detecting the temperature of said food. However, there are some breeds of squirrels that will be active at night. For example, it’s perfectly normal for flying squirrels to tend to be active at night. Other than that, most squirrels shouldn’t be troubling you at night.
In the off chance that you are bothered by noises coming from your attic such as scratching or running, it is more likely that you’re hearing a mouse, rat, raccoon, or an opossum. These creatures tend to look for food during nighttime so you should expect them to be active and noisy when you’re trying to sleep.