Hi Bkone,
That's normal because the browser will keep in its cache the video, the second person on another browser will watch the same video but not from your own browser cache.
Squid is not able to keep objects coming from CDNs like YouTube or URLs with '?' char.
To cache videos, images, etc... from CDN URLs, you should use a plugin that'll do the job for you.
You can try the SquidVideoBooster taking care 600+ websites including YouTube, DailyMotion, NetFlix, etc...
Link:
https://sourceforge.net/projects/squidvideosbooster/
Compatible Squid 2.7, 3.4 and 3.5.
Download this plugin and test, you'll see if it fits your needs ;o)
Bye Fred