Hello Dr. Somanna,
You should not catch any trouble from an unlisted or private video on YouTube. Unfortunately, I can't guarantee that for you.
The best way to avoid any copyright violation notices is to provide a credit in your video and a copyright notice for your video (the video work is yours no matter what other source materials you may use as long as you have secured permission to use those materials; including photography, stock footage, typefaces, music, special effects, etc.). If you're using Apple Loop "jingles" there is practically a 100% chance that somebody else has already posted a video using the jingle and that's where the problem lies: that the music is associated with somebody else's copyright video. You have a clear right to use the music. YouTube knows about Apple Loops and the licensing, but if you don't apply *your* copyright (and the music credit) they have problems with *their* legal standing. You can place the copyright and credit at the very end if you like on a "black screen" last frames (I'd use at least 2 seconds.) If you always do this for your videos, you may go public and monetize without violating copyright rules. (I prefer to put my copyright and credit notices on the front end of my videos before the actual "start" of the video. It's more efficient, and since I monetize, I get approved for monetization almost as quickly as my videos are uploaded and processed.)
The free audio files at the YouTube Content Audio Library (https://www.youtube.com/audiolibrary/music) do not require any kind of notice. You are encouraged by YouTube to use their music, free of charge, and no requirements for crediting. There is a fairly nice selection of quite usable music available there.
For the Apple jingles (and most other audio files), if you select the music in the FCPX Event Browser OR the storyline and select the Info inspector and select Audio from the drop down list at the bottom right corner of the inspector, you should be able to find who has the copyright for the jingle in use. Chances are, in the case of Apple jingles, it will simply be "Apple Inc."
HTH
Fox