Restore iOS 6 iTunes backup to iPhone 6 with iOS 8

TLDR: When restoring an old backup to a new phone, does the backup have to be done from the same number version OS as the OS the new phone will be restoring said backup to?

I have a few staff whose various iPhone 6's just came in. I'm in a bit of a conundrum and can use some help.

Most of them are on iOS 7 with either iPhone 4S, 5 or 5S with varying backups to iTunes or iCloud. One person has the 5 with iOS 6 (didn't like the 7 interface) but is upgrading to the iPhone 6, obviously with iOS 8. He backs up to iTunes on his personal Mac. How would I go about restoring his old settings and data from old phone to new one? Does the old phone have to be updated from iOS 6 to iOS 8 first then get a iTunes backup and restore to the new one? Updating the old phone to anything newer than iOS 7 is a problem for all of them. They have "legacy" applications that haven't yet been updated to support iOS 8 so it's my preference to keep their old devices on the current version OS they're on so they can use them for the particular things not yet supported on iOS 8.

Thanks.