Axl is referring to the Jack Adams, which is an award based solely on the regular season. It almost always goes to the coach of a team that has the top record or way over-performed expectations.
Hiller has been quietly excellent as a coach, employing interesting tactics and getting great results, but a team that goes from 3rd in a division to 2nd in a division isn't exactly going to earn a coach a Jack Adams. The Kings were already expected to make the playoffs, so he's not going to win.
My guess is that Carbery wins it, but maybe Hiller gets some consideration.