I would assume they recommend the same service Disney recommends. But even if the suggest someone else, you can use any service.
This is the one from the Disney page:
Together with independent childcare provider Kids Nite Out, the hotels at Walt Disney World Resort offer you the convenience of expert, one-to-one in-room babysitting for an additional cost. You can even reserve a childcare specialist to accompany you and your family during your visit to the Parks, providing a helping hand where needed. Available 24 hours a day, 7 days a week.
To contact Kid's Nite Out, Inc., please call (407) 828-0920, 8:00 a.m. to 9:00 p.m., 7 days a week. Guests under age 18 must have parent or guardian permission to call.
I forget the rate. I have it at home in my spreadsheet. We've used them before and will use again on this trip for PFTS.