I think you are handling it the right way for now - but there will soon be a tipping point where it distracts you to the extent you might not be happy coding this way at all.
If I were you, I would request a quick one-to-one with this person and explain my PoV calmly yet firmly. Team ownership of code etc is all fine but unless you give every developer enough space to put his work out, make mistakes and improve you will never build good code. This can be a friction area sooner rather than later.
(There is a totally different answer if this was on workplace.stackexchange. Figuring out the correct way to do code reviews is the easy bit. Convincing your co-worker to comply with this is a lot harder).
