I'm surprised I couldn't find another request for this, I suppose there may be one in the 910XT forum, but I was very disappointed not to see Garmin Connect show the total times on multisport activities from the 910XT.
It's been a 'feature' since dinosaurs ruled the planet so I wouldn't hold your breath waiting for a resolution.
As an aside, the only program I know that does this is Garmin Training Centre. None of the other websites or other programs I use or am aware off provide an overall time for a multisport activity. They all break out the individual legs and transitions.