Short answer: it's legal if you're using it for your personal needs (time-shifting) to view YouTube content offline when over-the-internet broadcasting is not available.
Long answer: according to decision of the Supreme Court of the United States on the case of Sony Corp. of America v. Universal City Studios (464 U.S. 417), from January 17, 1984: "...time shifting was a fair use, represented no substantial harm to the copyright holder..."
Converto.io is simply allowing users to watch YouTube content later (time-shifting) when Internet connection is not available. Our service is a DVR for YouTube, which can be compared to the case with Sony and Universal in 1984. If you have no Internet connection, it's totally fine to watch downloaded YouTube content.