If you would look closely, the rooftop tiles are a mixture of old and new. That is because the Old Town is highly rebuilt. Back in the early 1990s, the Old Town was bombed by the Serbian and Montenegrin forces. If you ever visit Dubrovnik, you'll see memorials and pictures of what happened back in 1991-1992. And if you walk the walls, you'll see that there are rooftops that have different shades of red: some are old, some are new. The new parts are where it has been rebuilt.
If you are in Dubrovnik during the summer, remember to take plenty of water when you visit the walls. It is hot. I was there in December and I still felt the sun's hot rays. I could only imagine when people visit this place in the middle of summer. There are little shops that sell water and snacks along the way, but they are heavily inflated so better bring your own.