Ikr. I was confused too and super shocked when I tried it out. This explanation I said I guarantee is true and from personal experience. f00kee guide about Arcanist even has some detail about it. I guess a description change would be cool to try and confuse less people . Ascendant is a dot effect if you look at the dot definition in the codex.
Also, it seems that the hirling doesn’t even have to attack for the Arcanist of both Hirling and Main character to combine in effect (double potencey). That’s how I was able to reach 20M power or more and how some people managed to reach 100M power. At least from my experience .