The bonus is additively applied to the critical chance of your weapons, after the effects of Point Strike and True Steel — but before the effects of Blood Rush. For example, under the effects of Cat's Eye, the Nukor with a critical chance of 3%, would increase to 63% without any other critical chance mods applied.
When Cat's Eye activates while under the effects of Blood Rush, Blood rush will multiply the critical chance after the modded crit chance is added with the Cat's Eye critical chance. This synergy can lead to staggeringly high critical strike damage due to orange and red crits.
Emplaced turrets (i.e. the Grineer Rampart) gain the ability to critically strike while under the effect of Cat's Eye.
While this also applies to weapons that cannot critically strike, these weapons often have a critical multiplier of 1.0 which yields no change in damage dealt.
Multiple instances of Cat's Eye do not stack.
The ability seems to trigger when an enemy is within at least 25 meters. (Clarification needed, requires further testing / source).
Cat's Eye shares its above critical hit behaviors with Arcane Avenger and Maiming Strike. With the bonus being additive instead of multiplicative.