I've done both of the Alliance in Zandalar quests that were available and there was none of that. One is Brann and you traveling through a bog then getting stuck with Blood Troll problems, the other one was just freeing Dark Iron troops and then having them deal with Horde troops.
The Intro quests to the actual zones have nothing to do with the Horde.
If you find out any specifics I would happily try to find it and take a look at it. I haven't seen any KT or Alliance on Zandalar except for a giant shipwreck on Zuldazar and the base in Nazmir.