The Web access uses what's on the Exchange Server.
Outlook on the Citrix doesn't have to use what's one the Exchange Server.
Sorry but this is something pretty basic they cover in the Exchange Server courses. I don't duplicate the courses but thought you may need the short version to refresh your memory.
https://www.google.com/search?hl=en&as_q=why+only+inbox+from+OWA+can+sync+back+to+MS+Outlook&as_epq=&as_oq=&as_eq=&as_nlo=&as_nhi=&lr=&cr=&as_qdr=all&as_sitesearch=&as_occt=any&safe=off&tbs=&as_filetype=&as_rights= finds prior discussions about why this happens and why IMAP or POP decisions matter.
But that's all at the courses you take to be an Exchange Administrator.
I have a user logging in to Citrix Server (on Windows 2003) to use Outlook 2007. In Outlook web access, he sees all his drafts in Draft Folder and can easily access them, but when he is Citrix, he can see the folder, but no messages.
I had him check Normal and Favorite Folders under View -> Navigation Pane as well as execute outlook /cleanviews but that didn't help.