Udyr E (Bear Stance Stun) Cooldown after Jax dodging it?

Alright so I've been playing top against a Jax as Udyr. I noticed that when I would stun him with my E, and he would have his E activated to dodge the stun, it would put my stun on him on a cooldown. Now I'm wondering, because the tooltip says: "Udyr's basic attacks Stun icon stun his target for 1 second. This effect cannot occur on the same target more than once every few seconds.", if it's :normal: that when the effect doesn't occur because he dodges (or blocks) it, how it still puts on the "timer" before you can actually stun Jax again?