I was reading about the Singleton design pattern and how to implement it thread-safe.

All went well until the authors said: “In reality, we need a lock only when initializing instance. That should occur only the first time instance is called”

and this is the implementation:

    Singleton* Singleton::instance() 
{
  if (instance == nullptr) {
    std::lock_guard<std::mutex> lock(mutex_);
    if (instance == nullptr) {
        Singleton* temp = new Singleton;
        instance = temp;
    }
  }
  return instance;
}

But I am concerned about saying that we only need a mutex while creating the instance. WHY?
Consider a case when you have a method inside the singleton class that modifies a common value based on a previous one. Am I right?