I also had this problem, and it involved not only Spotlight Search but searching within Contacts, too. I tried many of the suggestions here, and if they worked, they were temporary.
Finally, I think I have it figured out. It seems that even though I do not use iCloud for contacts, contacts within iCloud must be switched on in order for the searches to find my Outlook contacts. Said another way, I cannot have only Outlook contacts turned on, I must have iCloud contacts and thus multiple contact groups turned on even if I have no contacts in the other (iCloud in my case) group.
This is a bug. I have iOS 9.1 already so I'm not optimistic that it is entirely worked out for all configurations as those who have had luck with the beta version have hoped. Maybe next round...