Thank you, anonymous, but I must admit I can’t quite offer that much more information on caring for either form of ninetales.
Consider it like this: there are two types of pokémon evolution. Category A is when a pokémon changes drastically, to the point where their bodies differ so greatly from their predecessor that it’s impossible to care for the two in exactly the same way. This would include pokémon such as octillery, dragonite, huntail and gorebyss, most bug-types that undergo a cocoon stage (as well as the larvitar and bagon families, for that matter), and so on and so forth.
Then you have Category B, which consists entirely of pokémon that undergo a change, certainly, but not enough of one that they require an entirely different set of needs. Most pokémon belong to this category, including ninetales.
That having been said, most of the tips you read about in the vulpix entry will also apply to ninetales, with a few minor changes here and there. For example, keep in mind that your ninetales will be larger and more powerful, so be sure to increase the amount of food and water it receives daily. Likewise, scale up your training methods (that is, increase both the intensity and duration of its exercises) to accommodate its new power levels. Keep an eye on Alolan ninetales as well, as its new fairy-typing may require exercises geared towards training its magical potential (that is, add meditation to its regimen). And above all else, set aside time to help your ninetales maintain its tails, but be careful when brushing, as ninetales tend to be sensitive in that area. The idea that they would curse you if you pull one is a myth, but they will use either Flamethrower or Ice Beam on you (or a similar move, anyway) if you pull too hard. This makes grooming especially tricky for owners of Alolan ninetales, as their cloud-like tails tangle easily and trap quite a bit of debris. Just … be careful, readers.
The Pokédex According to Bill 