The exact meaning of 인터넷으로 is "through the internet", and it's proper in this case. For "on the internet" in this sentence, "인터넷에서" would be closer to the direct meaning. If you use "인터넷에", it becomes like "to the internet". It is used like "인터넷에 업로드 합니다." which means "I upload it to the internet".