I do emissary quests daily on my main, and every 3 days on my alt.
I had 2+todays to do on my alt and 0 on my main yesterday. 7.1 must have reset something, because I logged on to my alt, had 3 up, then logged on to my main and had the same 3 get copied over and were doable.
So log on to your alt with the most emissary quests up first this initial 7.1 login and get some free ones on all your characters, I guess.