I've got a fairly basic map with 3 layers: https://open-data-charter.carto.com/viz/844cc5da-34a9-11e6-810e-0e3ff518bd15/public_map.
For countries and cities I have selected infowindows to come up when you hover over either the countries or cities. In the Carto editor the infowindows appears for both cities and countries, however, in the public version of the map it only works for countries.