Turning on css aggregation is loading desktop css for every breakpoint.

See this issue -- I think it may be related: #1995938: Adaptivetheme should recompile aggregated mobile CSS during cache-clear without theme-settings resave

Also a problem we are experiencing, if aggregation is turned off all is fine, otherwise no amount of cache clearing will fix the adaptive issue with aggregation turned on - the desktop css remains active.

It's not real clear on what you mean by "desktop css remains active", do you mean the layout, your custom styles that you set in a responsive stylesheet etc?

If you mean styles (not layout), then yes you just need to save the theme settings again and those files get re-compiled, then clear the cache, they should load up.

I can see this file is exists, which means at some stage you did that already, otherwise there would be almost nothing in it:
http://visitgenevany.com/sites/default/files/adaptivetheme/gedp_at_subth...

Also I see:
http://visitgenevany.com/sites/default/files/adaptivetheme/gedp_at_subth...

So files are getting generated, but could be out of date. Try saving the theme settings THEN clear the cache.

It doesn't sound like a bug, but yeah, it's a pita behaviour that takes a module to work around (see the issue linked to above in #2).

Another possible cause is the weight of files being messed up, D7 has some issues but I can't know that unless I see the site with CSS aggregation ON, which clearly you don't want to do on the live site (understandable at the moment).

FYI "release = 7.x-3.x" is just a flag AT Core uses internally, the actual version is shown on the theme list page, where all themes are listed. If that is blank, then the it was pulled from git or the version string has been removed.

Assuming fixed?

Nevermind, I'm an idiot.