The 1860s as a starting decade is a popular conventional definition in English, in other languages "modern art" may be defined differently. But you are absolute

The 1860s as a starting decade is a popular conventional definition in English, in other languages "modern art" may be defined differently. But you are absolutely right, it makes more sense to call post-WW2 art the contemporary art or just postmodernism, because something that happened long before the birth of the half of the population of the planet isn't really "contemporary".