This makes a lot of sense when you consider more just how small a role your "conscious" mind plays in your cognition. It is really more of a control center, and has direct access to a very limited amount of your computing power. You can't consciously monitor all of your sensory neurons, or make use of the math processing your mind can do to throw a ball, or manually coordinate your muscles.

You can see the effect of this very clearly while talking. You don't plan out each word ahead of time, you go to say something and the words come out. You can choose to take a step back and plan things in more detail, but this isn't your default mode of operation. Also even then in your head the words tend to seem to just come from somewhere in a stream, like a little stimulation of what you were doing talking out loud.

It is not generally helpful to think of this as a different person, it is you and you stand to gain a lot from learning to trust it. Like how you trust it to be able to recall minute details of API documentation despite not being able to reproduce them in full. You can't recall every code problem you have ever solved, but in a way your subconscious has, and it has been refining them into a process to produce those incredible insights.