Eh it doesn't work like that. Youtube is actually very good at reliably determining it's you who's in that private window and Youtube is even known to track you with WebGL fingerprinting tactics to determine it's the same device. Doing things like spoofing your IP and useragent and using private mode browsing doesn't work.
(I still get recommendations in incognito windows for videos I recently played no matter how much I tweak Firefox and mess with the browser to defeat tracking!)
Edit: Since Youtube fingerprints your device with WebGL[0], it builds a shadow profile tied to that device, so that even in incognito/private sessions, you will get recommended videos that you recently watched, despite the anecdotal claims of others that they don't encounter this.
The only way to defeat that is to use an entirely separate device on a separate network that has a different fingerprint.