For the basics, you may wish to consult this post: http://bills-pokedex.tumblr.com/post/154749948831/what-are-different-care-methods-for-alolan-vulpix
Essentially, caring for an Alolan vulpix is very similar to a standard vulpix; the only difference is in its temperature tolerance and how one cares for its coat. However, so long as you keep it cool and brush it daily (especially right around the time it blows out one coat for another), then it should be fine.
Meanwhile, be sure to care for its psychological needs. Illegally obtained pokémon often go through some form of trauma, either due to the abuse involved in being captured or in being “cared for” thereafter. Evaluate this vulpix’s psychological health as soon as possible, and if it seems it’s developed any nervous habits, be sure to take the appropriate steps in order to reestablish trust. Always place this vulpix in a comfortable environment, approach it slowly and with non-threatening gestures, and provide plenty of affection throughout its stay with you.
Best of luck, anonymous!