First aid at Disneyland is provided by RNs employed by Disney. Anaheim Fire Department maintains a paramedic station in Downtown Disney as well as a nearby fire station. Care Ambulance provides ambulance transport for all of Anaheim, including Disneyland.
Your millage will vary by company.
I used to work at a (now gone) water park in Orange County. Seasonal work. We didn't have any protocols specifically (I honestly don't know how the admin side of that worked). Our responsibilities were to maintain/clean the first aid room, check the supplies, treat patients, write reports, and essentially the rest of the normal EMS things. Additionally, if needed, we did occasionally staff a lazy river life guard spot in front of first aid if the park was down guards. The schedule the first year was 6 hour shifts when the park was open full time (2 shifts) or 7 hour shifts (1 shift) when the park was working at reduced hours at the beginning and end of the season. The second season they just went with 1 11 hour shift. We could ask for a supervisor to come break us to either go get food at the food place in the park or heat up food if we brought food from home. Outside of that, there wasn't really any breaks, but we didn't really need any (you could "sneak" to the restroom next door or out to a churro cart for a drink refill if needed).
Technically speaking, requesting 911 had to go through the lead supervisor on duty at the time. I've never had any of my 3 requests denied, and there was additional background support that made this necessary (making sure that parking knew EMS was coming in, if possible moving the patient to the employee break room/employee entrance, etc).