Deterrence goes on cooldown regardless from whether it triggered or not.

How to recreate:

Get a team of 6x deterrence champions for normal hydra, one of them being shamael. Put shamael on the last spot.

Attack torment with the fastest champion. You'll have 20% for each champion to counterattack (including the champion you are attacking with). Note which champions didn't counterattack.

Now attack torment with any other champion. Champions that didn't counterattack on first turn have 0% of counterattacking now, because their deterrence is on cooldown. The only champion that can trigger deterrence is the one you are attacking with (because their deterrence cooldown got refreshed). All other champions that didn't counterattack on first attack basically lost their chance.