We've used Florida Leisure for the last few years and they look after us fantastically. Not the cheapest as they are very strict on the type of homes they manage so you know that there won't be any maintenance issues. I think this is becoming a big issue as more owners look to cut corners and save money. When we were there at Christmas it was very revealing to see the yards of some homes.
Also, I didn't think Disney allowed the use of their name to other company's so the link you gave would be a red flag to me and I'd avoid any company portraying themselves as Disney.