Universal has a plan, for power outage. Some things have backup generators, but most just use emergency lighting. Like others have said rides default to full brakes, and Yes operators are to manually E-stop the ride so it does not start up. Until it is known that power will not be restored guest on rides typically stay, unless they are in the station. Once operations determines a long restore time, then a full evac will begin.
Shops are to have guest leave and doors locked, restaurants can have people stay if there is ambient lighting. But food operations are shut down.
During opening season, we had several outages. Mostly due to Hulk, Poseidon, or doom causing too much draw on the service, typically only affected the individual transformers. It sucked when Hulk did because it would take out parts of POE too. My office we were required to stay in the dark, until our dept manager came from the USF offices.
The worse is a full hurricane closure. They told my department, prepare to stay on property. We would have cots set up on the soundstages. I was released to go home, but had to return as soon as possible after things were safe. My team leads stayed on site for 5 days.
As for Disney, yes the emergency lights are checked annually by RCFD, but some buildings i have heard have emergency lighting issues. Usually after 1 big incident, risk management takes over to replace/repair.