It all goes super smoothly and they are very efficient. They will give notes on your RV, Tent, Cabin etc, about the progression of the storm and what to expect and what they are wanting to do.
If it comes time to evacuate, you will be directed to head home if possible and they will refund you the rest of your stay. If that is not possible they will look to relocate you.
Yes, this CAN be a resort but it can also be a convention room with many other people (they will most likely try to avoid this route due to COVID issues but then again they may just warn you about what to expect). Keep in mind, this could be a regular Value resort and if you are in a Premium Meadows site or the like, you will have to ask them about the difference, since you paid more.
All in all we have been there through many evacuations and even as littles my kids never felt as though anything was up, because that is how smoothly and awesome it was. When transferred to another resort, you check in like normal and they will get you squared away ASAP. Each resort handles things differently as well. We have been to Deluxes during a hurricane and they had awesome activities set up for kids with characters and snacks, movies and the like. Moderates had arcades on free play as well as activities and snacks. Our family is too big for a Value but before kids when it happened and we were moved to one, they didn't do too much other than keep cast members in each building for questions and delivering flashlights to each room.
Each level of resort we have been in, has had flashlights delivered to the room, but at Values it was one, Moderates it was 2 and Club Level Deluxe it was one per person with extra batteries and Club Level Access at Moderates it was one per person.