I just tried; I only had one flying-type Pokemon in my party and Exp. Share was turned on, but my flying-type Pokemon was the only one to gain exp. points. I'm not sure if any other flying-type Pokemon in my party would have gained exp. points if I had others; perhaps you could tell me whether they do or not :D
Most likely it's because Yveltal was the only Pokemon in your party capable of participating in a Sky Battle. This does map over pretty well to a normal battle. With the EXP Share on, only Pokemon able to battle will gain EXP. Pokemon that have fainted, as well as unhatched eggs, will not gain EXP.
If you are interested in testing, I would recommend taking a second Flying type, or a Pokemon with the ability Levitate, and engaging in another Sky Battle.