For example, if a small base ship has disabled power regulator engages and gets an ion, and then receives another disabled power regulator from an attack so that there are two of them faceup, do they both flip when that ship does the ion maneuver from the first crit?

Yes

A bit more explanation: each critical damage card is treated as a separate ability with the same trigger. This means when you reach that timing (after executing an ion maneuver) both copies of Disabled Power Regulator are added to the Ability Que at the same time and can be resolved (repair this card) by the controlling player in any order.

I once ioned a ship after it had engaged. I then with another ship gave it the crit. It completed an ion maneuver the next turn and flipped the crit. It never received an ion from the crit.