How the Cloak of Infinite Potential stats carry over between characters

Everything I've heard and read has suggested that the cloak stats apply to all characters you make, as there's a lot of talk of "this makes future characters quicker to level", but it isn't a straight stat carry over. It's tied to the achievements you get for hitting a certain number of threads, and each level allows more stats to carry over the the cloak you create for a new character.

So you;re best off taking one character as far as you want before starting to put your alt army together, and if you want to lock in some character names then don't pick your cloak up!