Juggernauts' ion cannon doesn't seem to go off or at least, my ship only killed one member of the opposing fleet before it was destroyed 

Is this a bug, or does the ship need to survive for long time before it can charge its weapon?

The Juggernaut's Ion Wave ability is used at the strategic level. It's a fleet action visible in the panel on the left of the fleet interface. If your Juggernaut get into combat, I'm afraid it is too late to use the Ion Wave.

Which is a joke, since AI has faster reaction time then humans, especially when UI/controls are lagging. This action should've been accessible in battle start screen near "Retreat" command.

The-Cat-o-Nine-Tales wrote:

The Juggernaut's Ion Wave ability is used at the strategic level. It's a fleet action visible in the panel on the left of the fleet interface. If your Juggernaut get into combat, I'm afraid it is too late to use the Ion Wave.

Since I don't even know what a "fleet action" is unless we're talking about the things like guarding a solar system, it wasn't somethig I even remotely knew how to use...

Yes, Fleet Actions are command like Guard, Invade, Attack, or Auto-explore. A Juggernaut should have a new Fleet Action for the Ion Wave Ability after unlocking it.