Mei’s ultimate disappearing mid air is caused by latency:
[PROOF] Projectile Ults blocked by Lag
Just as Lucky44 said, Mei’s ultimate is a projectile that is thrown. One with a cast time. Ashe’s ultimate is an entity that is being summoned.
A better question would be why Zarya’s ultimate is the only projectile ultimate that doesn’t has a cast time. This is the only projectile ultimate that can’t be interrupted with stuns.