When you look at the "device" in place for the necklace... it seems pretty straight forward that the more Azerite you grind, the more attributes you will be able to select... and perhaps the higher the level of said attribute.
Since Blizzard was so trained on making each spec of the artifact weapon have it's own source of AP... it is likely this device will also have it's own pool of Azerite... meaning a grind for each spec. (as likely each spec will have different abilities and set bonuses.
This system is the same, exact system Legion has.. .a post max level, leveling system. The design of the neckpiece is really just a different graphical; way of seeing this but with 4 choices instead of three each level: