Bringing advisor into summer internship project
I think this situation seldom arises, so wouldn't call it typical. There might be university regulations that govern it, since your relationship to your advisor would change somewhat.
But I fear you are being a bit naive about the company's ownership of your results. It probably means that you can't publish without permission (and specific approval). It might mean, or imply, non-disclosure of what you learn. In the latter case, the company would need to establish a formal relationship with your advisor so that everyone understands and adheres to the ground rules.
I don't think there are problems necessarily, but you need to make sure that everybody in the process understands what is happening.