Have you checked settings for how Notes should open a meeting room. Look in File --> Preferences --> Sametime Meeting Rooms and section "Meeting Room Window". You have two options here, one for web and the other for embedded. 

You're right, I missed this setting. It still surprises me why browser window is there selected by default. Do you know per chance if there's a managed policy setting that can be set to have Sametime client selected by default?

meetings.launchURLRichClient=true; com.ibm.rtc.meetings.shelf, Enforce

Had real problems when links where for https instead of http as they are if you set your meeting server in SSL mode.
I wrote in my blog on my companiy site how I solved it

http://www.infoware.eu/open-sametime-meetings-in-ibm-notes-client-using-https-code-for-download

Regards
Mats