I suspect the time difference you are seeing is due to the fact that your two devices have different mechanisms for displaying the video. “Live” video requires a certain amount of buffering (from a few, to tens of seconds) to allow for stutter free playback.
Internet traffic arrives in “bursts of data” and your “connection speed” is the average amount of data received over a finite period of time. For video to appear smooth the video player will try to estimate your average connection speed and decide upon an arbitrary period of time to receive data before actually starting the playback, thus having some “pre-recorded” video to display if there is a slight lull in the data bursts for new video.
In your case there are two possible variables, the devices have different video playing mechanisms with different buffering strategies, and/or the internet connection speed of your phone is different to your wired connection.
If you want to check that both devices can see the current “internet” time open a browser on both and visit
GMT: Greenwich Mean Time - World Time / Time in every Time Zone