The trinkets will remove all "movement impairing effects and all effects which cause loss of control of your character." That includes Cyclone as you lose control of your character. The phrasing in quotes can be taken quite literally.

Truthfully the previous trinkets were based on limitations that didn't allow us to simply dispel any and all effects, and so the best three were chosen in each case. Now each player has the ability, which at the very best can be used every 2 minutes, to remove a crowd control ability. This is obviously going to result in some abilities that couldn't be removed before now being able to be removed. It's going to be something to adapt to, but the ability of yours that can now be removed is the same as the ability that's on you that you couldn't remove before.