I don't have this exact problem however the problem I have has basically the same effect. Start the strike and the other two just farm chests and never once make a move toward the strike. This happened 3 times where I finally just gave up and did the strike myself. Thankfully it was just the Devil's Lair and nothing particularly difficult but really why would you queue for a strike and then just farm chests? I did wait 15 minutes each time to see if these guys would eventually begin the strike but no go.