However, browsers on my own machines produce the old site. I tried multiple browsers and multiple devices (Ubuntu and Android), including some that never accessed the site, to make sure that the problem is not caused by DNS caching in the browser or in the machines. Using Hola or Tor as proxy from other countries, I correctly get the new site.
More strangely, some of the browsers occasionally shift between producing the one site or the other.
I suspect my ISP's DNS is giving crazy results, but how could I diagnose that?
Also, strangely, monitor.us is showing the site as going down, then up, several times a day, when as far as I can tell that is not happening. (It is a basic Wordpress site with, for now, no traffic.) That would suggest that monitor.us is also getting strange DNS values. How can I diagnose this?