First of all: I totally agree it’s not intuitive and it can easily be overlooked. I support the complaint! ;-) However, here’s how you get the final reward on iOS:
There is an “event icon” (for the lack of a better description) next to the fellowship icon. In the top-left part of the screen. When player clicks on it, it shows overall progress (for example something like 23/30 quests done). After finishing all the sequential quests, this is the place where player collects the building.