Mantle of the Talon King

You aren't granted this achievement right away. Once you hit exalted and have done the line, you must leave Spires and then return before a quest pops up to give you this achievement/follower.

Considering this achievement is account-wide (and therefore, can literally only be earned once ever), what happens to the follower with alts? Do you need to meet the criteria again anyway, or will it automatically be awarded to them?

If the follower is attached to the achievement itself and not the specific criteria, this can cause some complications.

That's not how achievements work. The rewards are account wide (sometimes), but you can still earn them on each character. For example, my rogue completed ICC years ago. If I make a new character and run them through ICC tomorrow, they will still get the achievement for completing ICC.