Then their web designer is not very good at what they do and shouldn't have a job in IT. This is basic (very basic) HTML. In fact they're using KRPano in the tour you link to and this in itself has just as many erroneous files as Panoweaver or Tourweaver.
It is as simple as removing the code from the second .html file and keeping the file structure the same (as output from Panoweaver or Tourweaver) The browser brand will make no difference at all (so long as you compiling with the most current build of Panoweaver or Tourweaver to create the panorama/tour) and so long as it has the current Flash plug-in installed (it's not a special plug-in just the same Flash plug-in that is required to view any Flash).
Understand the file structure is very important. If things aren't kept together you will get a message stating you need to update the Flash plug-in (and even when you do update the plug-in the same error will continue to show) this is because the file structure hasn't been maintained. All of the files including the .html have to stay together in the exact file structure.
This is where it may differ to KRPano, but this should pose no problem to anybody who has an ounce of .html skill.
Panoweaver and Tourweaver have been around a lot longer than these other viewers and people use them world over. Your/their web designer needs to get a grip on basic coding. Or perhaps it needs to be explained to them in a better way.
Bottom line, if you don't mess up the file structure the tour will work.