Remote Desktop users are using the browser as setup inside the host ( server , or citrix ) app.
The server admin can define options like
browser settings ( enhanced security settings of IE )
Virus scanner integration
and also what browser is available ( IE 7-8-9-10 ).
Those browser act different in there rendering
The IE-XXX compatibilty-mode are controllable by your application
http://msdn.microsoft.com/library/cc817574.aspx
Per Page:
<meta http-equiv="X-UA-Compatible" content="IE=8"/>
The page will be always rendered in “IE8 Standards mode” even when no “!DOCTYPE” is existing in html
<meta http-equiv="X-UA-Compatible" content="IE=EmulateIE9"/>
The page will be always rendered in “IE9 Standards mode” even when no “!DOCTYPE” is existing in html
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
The page will be always rendered in “IE9 Standards mode” even when no “!DOCTYPE” is existing in html
<meta http-equiv="X-UA-Compatible" content="IE=edge"/>
At this configuration the highest available version of the IE rendering engine will be used . It does not care if a “!DOCTYPE” was used or not. this function is comparable with “IE=7” and “IE=8”. This is used to be compatible with the highest IE version.
So i think you do not need to care about RDP or Citrix Hosts but to support the using IE in the right mode.