I know this problem. You must have saved the same file in both profiles, owner and the secondary where you want to use it. In both profiles under files>your_device_name_>ringtones. This should solve the issue. Don't know exactly why this is needed but it could be related to the fact phone calls are forewarded from owner to the 2nd profile.
Edit: You don't have to set the same ringtones for standard or a specific contact in both profiles, you can use different ones in every profile. It's just important to have saved the file used in the secondary profile in owner as well as in the used profile.