Same here!
I have the issue on 3 devices (one 6s and two 5s) and my brother as well on his iPhone 6.
So I had to contact the helpdesk and they had no clue. Then they forwarded me to the 2nd level support. I had to reset the devices and set them up as new device (without using a backup) only the contacts have been synced via icloud.
The issue persist. I can choose custom ringtones for my contacts. The ringtone is assigned correctly but when the contact calls the standard ringtone is played instead of the assigned one.
I had to make videos and pictures on how i change the ringtone and send it to the analyst. The analyst has now send the documentation to the technical support. Need to wait for them to reply.
Guess we might see an update for iOs 10 coming up.
The annoying thing is that this seems to be an issue which has been reported in the Beta versions already.
Sad to see that Apple has lost the appetite not only on bringing real innovations but also dropped the sens for perfection.