I’m not a jitsi expert here, so I could be wrong… but:
The Jitsi server does not do any processing of the video stream. For 2 people (1-1 communications), they send streams directly to each other. For 3+ people, the server is nothing more than a relay – it receives and forwards streams, but doesn’t do any alterations.
Watermarking the live stream would require a change to the video stream that goes to each client. As the client decodes and renders each video, it would be uniquely watermarked.
Locally saved videos are a different (and easier) problem. If you have this enabled, then you effectively store a video file on your local server; this video is available after the conference ends. After the conference is over, you can post-process that however you want, including re-encoding it with a unique per-user watermark. FFmpeg makes this pretty ease (see http://ksloan.net/watermarking-videos-from-the-command-line-using-ffmpeg-filters/).