It was switched on after landing:
http://www.unfinishedman.com/wp-content/uploads/2012/10/Felix-Baumgartner-Zenith-El-Primero-Stratos-Watch.jpg
And yes, he had another device called Cypres right near the classic Cypres:
http://www.wall-pix.net/albums/art-space/00025885.Felix.Baumgartner.jpg
It seems that BBC just used video editing and some scenes are not from the real jump.